# Multiple parameter curve fitting with complex numbers

I have some problems with curve fitting, where my independent variable f (frequency) is real but the dependent variable is complex. I want to fit the curve with a given equation and to find the missing parameters (two different curves with two different dependent complex variables)

My data are in a .txt file and I import them. I joined them, or is it better to take them one by one?

I'm not sure to make it if "Map" for both together or one by one without all them and just fit?

The output should be the plotted data with the curve fitting and the estimated parameters of the function.

Is it possible with real and imaginary part or is it better/only possible with the absolute value as input?

My file until now is:

    \[Rho]0 := 1.199;
\[Sigma] := 40926.55;
\[Omega] := 2*Pi*f;
\[Eta] := 1.81*10^-5;
\[Kappa] := 1.4;
Pr := 0.72;
B := Sqrt[Pr];
P0 := 101325;

rawKomp = Import["Desktop/KompMneu.txt", "Data"];
(* Take the Re and Im part and put together*)
fmtKomp = Map[{#[[1]], #[[2]] + I*#[[3]]} &, rawKomp];
rawRho = Import["Desktop/Rho.txt", "Data"];
(* Take the Re and Im part and put together*)
fmtRho = Map[{#[[1]], #[[2]] + I*#[[3]]} &, rawRho];
(* Join to one data*)
fmtKompRho = MapThread[Join, {fmtKomp, fmtRho}];
result = Map[(f = #[[1]]; KompM = #[[2]]; \[Rho]eff = #[[4]];
KompM == ((P0*\[Kappa])/\[Phi])/(\[Kappa] - (\[Kappa] -
1) (1 + (8*\[Eta])/(
I (\[Omega]*B^2*\[Xi]^2*\[Rho]0))*(1 +
I (\[Omega]*B^2*\[Rho]0*\[Xi]^2)/(16*\[Eta]))^(1/2))^-1);
\[Rho]eff == ((\[Rho]0*\[Alpha])/\[Phi])*(1 + (\[Phi]*\[Sigma])/(
I (\[Omega]*\[Rho]0*\[Alpha]))*(1 +
I (4*\[Omega]*\[Rho]0*\[Eta]*\[Alpha]^2)/(\[Sigma]^2*\
\[Phi]^2*\[Lambda]^2))^(1/2));
nlm =
NonlinearModelFit[fmtKomp,
KompM == ((P0*\[Kappa])/\[Phi])/(\[Kappa] - (\[Kappa] -
1) (1 + (8*\[Eta])/(
I (\[Omega]*B^2*\[Xi]^2*\[Rho]0))*(1 +
I (\[Omega]*B^2*\[Rho]0*\[Xi]^2)/(16*\[Eta]))^(
1/2))^-1), {\[Xi], \[Phi]}, f]
{}) &, fmtKompRho];


For the fit, I'm not sure if the dependent input should be real and imaginary part or the absolute value.

Second cloumn values are related with this equation:

KompM == ((P0*\[Kappa])/\[Phi])/(\[Kappa] - (\[Kappa] -
1) (1 + (8*\[Eta])/(
I (\[Omega]*B^2*\[Xi]^2*\[Rho]0))*(1 +
I (\[Omega]*B^2*\[Rho]0*\[Xi]^2)/(16*\[Eta]))^(1/2))^-1)


with search for [Xi] and [Phi]

Fourth cloumn values are related with this equation:

\[Rho]eff == ((\[Rho]0*\[Alpha])/\[Phi])*(1 + (\[Phi]*\[Sigma])/(
I (\[Omega]*\[Rho]0*\[Alpha]))*(1 +
I (4*\[Omega]*\[Rho]0*\[Eta]*\[Alpha]^2)/(\[Sigma]^2*\[Phi]^2*\
\[Lambda]^2))^(1/2))


with search for \[Alpha], \[Phi] and \[Lambda]

Restrictions are: 1 < \[Alpha] < 4

0 < \[Phi] < 1

1*10^-6 < \[Lambda] < 1*10^-3

1*10^-6 < \[Xi] < 1*10^-3

Many thanks for concrete help!

PS. I already tried a lot with NLMF, but didn't work :(

extract of my data:

{2000, 7.495132*^-6 - 2.905868*^-6*I, 2000, 2.8457991495590997 - 1.1581370520116134*I} {2001, 7.523548*^-6 - 2.914476*^-6*I, 2001, 2.858304261624532 - 1.1687498198289332*I} {2002, 7.5122*^-6 - 2.93425*^-6*I, 2002, 2.860108647518152 - 1.1672351759527078*I} {2003, 7.495931*^-6 - 2.941156*^-6*I, 2003, 2.8613357931205097 - 1.1677630072443932*I} {2004, 7.500676*^-6 - 2.943248*^-6*I, 2004, 2.8650190833881313 - 1.159968644414602*I} {2005, 7.50707*^-6 - 2.942191*^-6*I, 2005, 2.8679628964823345 - 1.1701313097831112*I} {2006, 7.525663*^-6 - 2.905331*^-6*I, 2006, 2.8946350022956513 - 1.1660569860147378*I} {2007, 7.521733*^-6 - 2.905645*^-6*I, 2007, 2.9076754036664685 - 1.1593147448053216*I} {2008, 7.524654*^-6 - 2.921134*^-6*I, 2008, 2.9178186871461844 - 1.1692175553021837*I} {2009, 7.442054*^-6 - 2.928626*^-6*I, 2009, 2.9058750005363203 - 1.1688372400146436*I} {2010, 7.441113*^-6 - 2.916094*^-6*I, 2010, 2.9154310656748006 - 1.1559241802440834*I} {2011, 7.439356*^-6 - 2.869886*^-6*I, 2011, 2.925660003190935 - 1.1471310204697107*I} {2012, 7.421177*^-6 - 2.874727*^-6*I, 2012, 2.9286463526511963 - 1.1551842071073424*I} {2013, 7.428163*^-6 - 2.930967*^-6*I, 2013, 2.9386680228883573 - 1.1772206248192012*I} {2014, 7.394478*^-6 - 2.886917*^-6*I, 2014, 2.9367045243631567 - 1.157098344979481*I} {2015, 7.384815*^-6 - 2.915217*^-6*I, 2015, 2.9221637411423442 - 1.1549766318272674*I} {2016, 7.429573*^-6 - 2.909497*^-6*I, 2016, 2.9514150355906685 - 1.1623418296212267*I} {2017, 7.408368*^-6 - 2.966152*^-6*I, 2017, 2.9523391532916374 - 1.1810572897141929*I} {2018, 7.344352*^-6 - 2.902669*^-6*I, 2018, 2.974845084302254 - 1.160087864492292*I} {2019, 7.346345*^-6 - 2.884528*^-6*I, 2019, 2.9827612303253193 - 1.1507915820822794*I} {2020, 7.394507*^-6 - 2.911018*^-6*I, 2020, 2.9968541795706067 - 1.151509672290089*I} {2021, 7.477878*^-6 - 2.971254*^-6*I, 2021, 3.044150524577359 - 1.1920954586433354*I} {2022, 7.452694*^-6 - 2.892408*^-6*I, 2022, 3.021391149545703 - 1.1718101812159232*I} {2023, 7.379359*^-6 - 2.89546*^-6*I, 2023, 2.9971988728179513 - 1.1627813497977413*I} {2024, 7.371485*^-6 - 2.900114*^-6*I, 2024, 2.9986234885018437 - 1.180398798039393*I} {2025, 7.38355*^-6 - 2.911429*^-6*I, 2025, 3.0105129501350896 - 1.1744958632701281*I} {2026, 7.322522*^-6 - 2.93499*^-6*I, 2026, 3.019651457503094 - 1.1671545388881752*I} {2027, 7.380005*^-6 - 2.892523*^-6*I, 2027, 3.0317867575472857 - 1.1654217902794963*I} {2028, 7.36419*^-6 - 2.880249*^-6*I, 2028, 3.039307793041939 - 1.1598323540676279*I} {2029, 7.394916*^-6 - 2.947811*^-6*I, 2029, 3.0445081014416933 - 1.1842487386860905*I} {2030, 7.397766*^-6 - 2.878933*^-6*I, 2030, 3.0707571291789493 - 1.1736831960602299*I} {2031, 7.348815*^-6 - 2.885062*^-6*I, 2031, 3.0565842332604563 - 1.1600163592050068*I} {2032, 7.361899*^-6 - 2.922902*^-6*I, 2032, 3.056165067997835 - 1.2011522036878661*I} {2033, 7.313552*^-6 - 2.894793*^-6*I, 2033, 3.0637766290407535 - 1.1900683694393501*I} {2034, 7.346721*^-6 - 2.874572*^-6*I, 2034, 3.0743003638605693 - 1.1795196482725865*I} {2035, 7.294209*^-6 - 2.881883*^-6*I, 2035, 3.082437544093112 - 1.1646423923943423*I} {2036, 7.266627*^-6 - 2.870893*^-6*I, 2036, 3.09369908396027 - 1.1592655193101675*I} {2037, 7.287074*^-6 - 2.889181*^-6*I, 2037, 3.0981103393371954 - 1.1671363449996406*I} {2038, 7.306574*^-6 - 2.889676*^-6*I, 2038, 3.0850590115322816 - 1.1879807667554907*I} {2039, 7.311147*^-6 - 2.892978*^-6*I, 2039, 3.096176045672851 - 1.1871441446678035*I} {2040, 7.289898*^-6 - 2.904233*^-6*I, 2040, 3.0950530060368115 - 1.1892380721451732*I} {2041, 7.365602*^-6 - 2.925616*^-6*I, 2041, 3.1216477221734364 - 1.205616391796217*I} {2042, 7.408672*^-6 - 2.906205*^-6*I, 2042, 3.162532389447015 - 1.2283924109987645*I} {2043, 7.328532*^-6 - 2.875041*^-6*I, 2043, 3.1719998805306133 - 1.2003668524550262*I} {2044, 7.321471*^-6 - 2.901961*^-6*I, 2044, 3.158375011149237 - 1.1967411501732488*I} {2045, 7.299224*^-6 - 2.902464*^-6*I, 2045, 3.1453402415562306 - 1.1985863933238132*I} {2046, 7.250666*^-6 - 2.882025*^-6*I, 2046, 3.141614787245539 - 1.185008528843694*I} {2047, 7.275414*^-6 - 2.868046*^-6*I, 2047, 3.1718142302327457 - 1.1886971674493132*I} {2048, 7.273855*^-6 - 2.909328*^-6*I, 2048, 3.169175526724791 - 1.209816692377188*I} {2049, 7.297497*^-6 - 2.87047*^-6*I, 2049, 3.178584023639635 - 1.1880069620017926*I} {2050, 7.287927*^-6 - 2.872364*^-6*I, 2050, 3.180356431224294 - 1.1931114531358609*I} {2051, 7.280325*^-6 - 2.881914*^-6*I, 2051, 3.1801903458236085 - 1.2065161738585939*I} {2052, 7.236789*^-6 - 2.871143*^-6*I, 2052, 3.1745563897121634 - 1.2022194118221021*I} {2053, 7.296309*^-6 - 2.917024*^-6*I, 2053, 3.2120879321256934 - 1.2221048434751642*I} {2054, 7.3124*^-6 - 2.864913*^-6*I, 2054, 3.224237656636732 - 1.2052280215940832*I} {2055, 7.28114*^-6 - 2.891531*^-6*I, 2055, 3.218018732744165 - 1.2117552909697484*I} {2056, 7.289919*^-6 - 2.886004*^-6*I, 2056, 3.2326254683521154 - 1.2122481093534634*I} {2057, 7.257601*^-6 - 2.897211*^-6*I, 2057, 3.217962115089541 - 1.2223699532828294*I} {2058, 7.260279*^-6 - 2.881104*^-6*I, 2058, 3.2389203796739485 - 1.2117173816647495*I} {2059, 7.281302*^-6 - 2.861952*^-6*I, 2059, 3.260495277360314 - 1.2138033061663234*I} {2060, 7.270785*^-6 - 2.890771*^-6*I, 2060, 3.2577983257075065 - 1.2158486725791715*I} {2061, 7.256613*^-6 - 2.875408*^-6*I, 2061, 3.2625527673023496 - 1.2136015768796173*I} {2062, 7.245962*^-6 - 2.859256*^-6*I, 2062, 3.27096746675466 - 1.2101440769826899*I} {2063, 7.293555*^-6 - 2.82496*^-6*I, 2063, 3.287464608385816 - 1.1912499453014118*I} {2064, 7.248404*^-6 - 2.851234*^-6*I, 2064, 3.2936504073877377 - 1.2082986088888814*I} {2065, 7.248008*^-6 - 2.852582*^-6*I, 2065, 3.2936528663215046 - 1.210822495936873*I} {2066, 7.233226*^-6 - 2.845537*^-6*I, 2066, 3.2842866302743725 - 1.2007265537232628*I} {2067, 7.221098*^-6 - 2.874587*^-6*I, 2067, 3.280386421370818 - 1.2091114769669498*I} {2068, 7.240196*^-6 - 2.863706*^-6*I, 2068, 3.3045893216727005 - 1.2194093299108808*I} {2069, 7.227762*^-6 - 2.8689*^-6*I, 2069, 3.312285777463507 - 1.2201469359664936*I} {2070, 7.193955*^-6 - 2.884132*^-6*I, 2070, 3.303696075525526 - 1.2210201178817757*I} {2071, 7.223433*^-6 - 2.880529*^-6*I, 2071, 3.3339808861870446 - 1.2122663537059482*I} {2072, 7.180459*^-6 - 2.876621*^-6*I, 2072, 3.314909839193502 - 1.223304537211776*I} {2073, 7.192802*^-6 - 2.838826*^-6*I, 2073, 3.331851728674295 - 1.2167252584482828*I} {2074, 7.224401*^-6 - 2.865291*^-6*I, 2074, 3.3453462401084244 - 1.2296153265407799*I} {2075, 7.210489*^-6 - 2.882658*^-6*I, 2075, 3.344494384812742 - 1.239014085561632*I} {2076, 7.184461*^-6 - 2.865467*^-6*I, 2076, 3.3494164976550675 - 1.234146433376548*I} {2077, 7.183453*^-6 - 2.873138*^-6*I, 2077, 3.362455110047014 - 1.2413621828649037*I} {2078, 7.188311*^-6 - 2.888521*^-6*I, 2078, 3.363346360265745 - 1.2538309594488288*I} {2079, 7.18906*^-6 - 2.901187*^-6*I, 2079, 3.3641307561332123 - 1.2665587842429873*I} {2080, 7.17776*^-6 - 2.882755*^-6*I, 2080, 3.3868277752374714 - 1.2592401315517774*I} {2081, 7.192649*^-6 - 2.86616*^-6*I, 2081, 3.393108319692287 - 1.231197787784403*I} {2082, 7.157993*^-6 - 2.864645*^-6*I, 2082, 3.3844674147729523 - 1.234486629895243*I} {2083, 7.173309*^-6 - 2.851179*^-6*I, 2083, 3.402455898166957 - 1.2319973930595705*I} {2084, 7.186671*^-6 - 2.83411*^-6*I, 2084, 3.4199758173260735 - 1.2437162826859252*I} {2085, 7.204534*^-6 - 2.873051*^-6*I, 2085, 3.411232099474241 - 1.2570348074910758*I} {2086, 7.168827*^-6 - 2.884495*^-6*I, 2086, 3.4138717092710267 - 1.2406291303693877*I} {2087, 7.142598*^-6 - 2.878513*^-6*I, 2087, 3.3936938650460067 - 1.2478515153881884*I} {2088, 7.112094*^-6 - 2.847112*^-6*I, 2088, 3.396689099859415 - 1.2415746969223473*I} {2089, 7.084803*^-6 - 2.856904*^-6*I, 2089, 3.3948605999678065 - 1.2314797525262344*I} {2090, 7.172837*^-6 - 2.838187*^-6*I, 2090, 3.448308585224038 - 1.2372132800810134*I} {2091, 7.145921*^-6 - 2.829776*^-6*I, 2091, 3.44484877972524 - 1.2369806154799745*I} {2092, 7.133623*^-6 - 2.844192*^-6*I, 2092, 3.446931852758502 - 1.2409003946951613*I} {2093, 7.163362*^-6 - 2.855653*^-6*I, 2093, 3.450930266047053 - 1.2481418299076337*I} {2094, 7.142563*^-6 - 2.852699*^-6*I, 2094, 3.4695642422938917 - 1.2427763691902936*I} {2095, 7.126612*^-6 - 2.845983*^-6*I, 2095, 3.4797030332494057 - 1.241429685184697*I} {2096, 7.127896*^-6 - 2.824535*^-6*I, 2096, 3.48557203484632 - 1.234375931760975*I} {2097, 7.127572*^-6 - 2.861112*^-6*I, 2097, 3.469190155204995 - 1.259853355940821*I} {2098, 7.104591*^-6 - 2.861577*^-6*I, 2098, 3.462195464269015 - 1.2650719290410364*I} {2099, 7.134373*^-6 - 2.868195*^-6*I, 2099, 3.468783222679186 - 1.2763654737660217*I} {2100, 7.124315*^-6 - 2.834702*^-6*I, 2100, 3.490234717959473 - 1.249697420170592*I} {2101, 7.117325*^-6 - 2.837313*^-6*I, 2101, 3.5046330668434797 - 1.2555082619086886*I} {2102, 7.09521*^-6 - 2.847509*^-6*I, 2102, 3.5010108501291826 - 1.2574500296177762*I} {2103, 7.068239*^-6 - 2.865387*^-6*I, 2103, 3.4842363843091557 - 1.2584652530693017*I} {2104, 7.106215*^-6 - 2.851826*^-6*I, 2104, 3.4989924516884554 - 1.2685354827466713*I} {2105, 7.100236*^-6 - 2.852559*^-6*I, 2105, 3.512989423182069 - 1.2756274375379641*I} {2106, 7.10942*^-6 - 2.85067*^-6*I, 2106, 3.522495509283315 - 1.2787752906355292*I} {2107, 7.10425*^-6 - 2.853309*^-6*I, 2107, 3.538420774293085 - 1.269975358911375*I} {2108, 7.07183*^-6 - 2.860673*^-6*I, 2108, 3.52679571439129 - 1.2724239230384646*I} {2109, 7.060374*^-6 - 2.830646*^-6*I, 2109, 3.530140050217009 - 1.259076696689758*I} {2110, 7.049042*^-6 - 2.864075*^-6*I, 2110, 3.526401245207149 - 1.2787101668024807*I} {2111, 7.081651*^-6 - 2.823909*^-6*I, 2111, 3.5360741465811243 - 1.2598246248635292*I} {2112, 7.085495*^-6 - 2.846555*^-6*I, 2112, 3.5545433655028043 - 1.2697545775337138*I} {2113, 7.08096*^-6 - 2.846432*^-6*I, 2113, 3.571132246901645 - 1.2763295322355055*I} {2114, 7.060658*^-6 - 2.847598*^-6*I, 2114, 3.5722288670749687 - 1.2747057469706589*I} {2115, 7.055437*^-6 - 2.844852*^-6*I, 2115, 3.574768705811392 - 1.2695739706480047*I} {2116, 7.076917*^-6 - 2.824114*^-6*I, 2116, 3.6015219293887566 - 1.2939351905736858*I} {2117, 7.087659*^-6 - 2.825328*^-6*I, 2117, 3.596549515383386 - 1.2815758371338413*I} {2118, 7.035001*^-6 - 2.833016*^-6*I, 2118, 3.577397284939306 - 1.2715639840618762*I} {2119, 7.049455*^-6 - 2.855892*^-6*I, 2119, 3.5900667532823682 - 1.299120850900452*I} {2120, 7.026281*^-6 - 2.85172*^-6*I, 2120, 3.5944421716492125 - 1.2864191429163558*I} {2121, 7.071693*^-6 - 2.846427*^-6*I, 2121, 3.60744839087522 - 1.2961904045036712*I} {2122, 7.063791*^-6 - 2.845137*^-6*I, 2122, 3.6101314442467536 - 1.29982515854867*I} {2123, 7.0411*^-6 - 2.826877*^-6*I, 2123, 3.6173257883192336 - 1.2939157143154014*I} {2124, 7.051438*^-6 - 2.823959*^-6*I, 2124, 3.630259718660997 - 1.2916323604178737*I} {2125, 7.033196*^-6 - 2.825102*^-6*I, 2125, 3.632579005729648 - 1.2878582030069397*I} {2126, 7.015494*^-6 - 2.83661*^-6*I, 2126, 3.639108832343987 - 1.2865339693187958*I} {2127, 7.022227*^-6 - 2.842273*^-6*I, 2127, 3.6454677015466896 - 1.2899824679641176*I} {2128, 7.018888*^-6 - 2.830218*^-6*I, 2128, 3.6332341180401175 - 1.2961468757227599*I} {2129, 7.025758*^-6 - 2.838197*^-6*I, 2129, 3.648380728464723 - 1.2924051392001095*I} {2130, 7.023952*^-6 - 2.825806*^-6*I, 2130, 3.6571754188564998 - 1.3010335563233906*I} {2131, 6.996865*^-6 - 2.82802*^-6*I, 2131, 3.649080468800596 - 1.2853683367932953*I} {2132, 7.012412*^-6 - 2.82621*^-6*I, 2132, 3.6727793937798454 - 1.2985554546514684*I} {2133, 7.014517*^-6 - 2.843414*^-6*I, 2133, 3.669731154014381 - 1.3056920876449774*I} {2134, 7.015398*^-6 - 2.828791*^-6*I, 2134, 3.6762719347664805 - 1.3028374713328856*I} {2135, 6.993861*^-6 - 2.828622*^-6*I, 2135, 3.6707950267545204 - 1.300689904497961*I} {2136, 7.012558*^-6 - 2.835998*^-6*I, 2136, 3.685487817026265 - 1.308708066249431*I} {2137, 6.998404*^-6 - 2.826854*^-6*I, 2137, 3.691254830951492 - 1.3037619705398962*I} {2138, 6.991028*^-6 - 2.835125*^-6*I, 2138, 3.6864045178747693 - 1.3065285577823158*I} {2139, 6.987892*^-6 - 2.818668*^-6*I, 2139, 3.6966704372209844 - 1.30688563876902*I} {2140, 6.984183*^-6 - 2.832233*^-6*I, 2140, 3.6968769390300085 - 1.3161346226465318*I} {2141, 6.990634*^-6 - 2.824747*^-6*I, 2141, 3.7094122067684707 - 1.312270475294366*I} {2142, 6.977548*^-6 - 2.825761*^-6*I, 2142, 3.710605616340883 - 1.3139229463955435*I} {2143, 6.977187*^-6 - 2.82314*^-6*I, 2143, 3.7208852838265556 - 1.3223999855783337*I} {2144, 6.977968*^-6 - 2.810149*^-6*I, 2144, 3.7230022510834573 - 1.3086699018858217*I} {2145, 6.995282*^-6 - 2.803478*^-6*I, 2145, 3.7423797262928025 - 1.30354400752805*I} {2146, 6.984573*^-6 - 2.822967*^-6*I, 2146, 3.7439914944716506 - 1.3229952184565767*I} {2147, 6.944256*^-6 - 2.836913*^-6*I, 2147, 3.727938163541516 - 1.3176778888383112*I} {2148, 6.982781*^-6 - 2.825124*^-6*I, 2148, 3.7469817265378436 - 1.3218208753930805*I} {2149, 6.961982*^-6 - 2.824048*^-6*I, 2149, 3.7468611538942085 - 1.3229307743302263*I} {2150, 6.957276*^-6 - 2.806833*^-6*I, 2150, 3.7620082377066257 - 1.3210492304668608*I} {2151, 6.977681*^-6 - 2.813285*^-6*I, 2151, 3.770356105344021 - 1.3332687802820016*I} {2152, 6.959489*^-6 - 2.813379*^-6*I, 2152, 3.773662671477991 - 1.3332804777125644*I} {2153, 6.954737*^-6 - 2.811938*^-6*I, 2153, 3.773943469213397 - 1.327804566250375*I} {2154, 6.951477*^-6 - 2.825623*^-6*I, 2154, 3.7693314233589144 - 1.3368804679487694*I} {2155, 6.970399*^-6 - 2.818763*^-6*I, 2155, 3.804557409698832 - 1.350643401495856*I} {2156, 6.968164*^-6 - 2.812937*^-6*I, 2156, 3.7929822936540134 - 1.3433223171112545*I} {2157, 6.943806*^-6 - 2.819825*^-6*I, 2157, 3.787561946874454 - 1.3433242494959041*I} {2158, 6.944856*^-6 - 2.813281*^-6*I, 2158, 3.796143555930769 - 1.3407165691092349*I} {2159, 6.946764*^-6 - 2.81564*^-6*I, 2159, 3.805863681564453 - 1.3457861878110782*I} {2160, 6.92189*^-6 - 2.817112*^-6*I, 2160, 3.8046658559315625 - 1.3459131477081423*I} {2161, 6.939267*^-6 - 2.804477*^-6*I, 2161, 3.814167747064259 - 1.34609586457654*I} {2162, 6.92874*^-6 - 2.818332*^-6*I, 2162, 3.812873581835853 - 1.3545884373262465*I} {2163, 6.936496*^-6 - 2.806905*^-6*I, 2163, 3.824086179755113 - 1.3476878663153715*I} {2164, 6.917792*^-6 - 2.824877*^-6*I, 2164, 3.825478376378739 - 1.3520171595487482*I} {2165, 6.934387*^-6 - 2.824357*^-6*I, 2165, 3.8480371800531556 - 1.3621777265514086*I} {2166, 6.918327*^-6 - 2.821069*^-6*I, 2166, 3.8428068737380787 - 1.3532925125253934*I} {2167, 6.916673*^-6 - 2.819186*^-6*I, 2167, 3.848015323625263 - 1.3695514600804202*I} {2168, 6.922018*^-6 - 2.796333*^-6*I, 2168, 3.838931773992248 - 1.3663589046793032*I} {2169, 6.913219*^-6 - 2.816394*^-6*I, 2169, 3.8509768346752704 - 1.3590703559562052*I} {2170, 6.90216*^-6 - 2.809711*^-6*I, 2170, 3.8550742690972655 - 1.3636029310618143*I} {2171, 6.90881*^-6 - 2.796066*^-6*I, 2171, 3.857359796085168 - 1.3584561866664808*I} {2172, 6.907162*^-6 - 2.816351*^-6*I, 2172, 3.8625710179501973 - 1.3695517699543973*I} {2173, 6.893353*^-6 - 2.810988*^-6*I, 2173, 3.8680017451044266 - 1.3727295339034238*I} {2174, 6.897265*^-6 - 2.805433*^-6*I, 2174, 3.879903439682928 - 1.3707927772528417*I} {2175, 6.889423*^-6 - 2.819827*^-6*I, 2175, 3.8816138914903826 - 1.3663579919453444*I} {2176, 6.90397*^-6 - 2.817897*^-6*I, 2176, 3.890493019355193 - 1.3650173912712535*I} {2177, 6.900028*^-6 - 2.809628*^-6*I, 2177, 3.8884208333451693 - 1.3656817707247038*I} {2178, 6.895842*^-6 - 2.798522*^-6*I, 2178, 3.903948530600895 - 1.380758661843973*I} {2179, 6.901945*^-6 - 2.805944*^-6*I, 2179, 3.9052168253041453 - 1.384032957056686*I} {2180, 6.884092*^-6 - 2.809101*^-6*I, 2180, 3.9015498956315398 - 1.3824476833373767*I} {2181, 6.866092*^-6 - 2.802444*^-6*I, 2181, 3.8974428432058548 - 1.3759249588648823*I} {2182, 6.900282*^-6 - 2.805445*^-6*I, 2182, 3.91997034129632 - 1.3888425389868426*I} {2183, 6.876723*^-6 - 2.799295*^-6*I, 2183, 3.9158563572250022 - 1.3831596918917486*I} {2184, 6.867522*^-6 - 2.807662*^-6*I, 2184, 3.91962597996332 - 1.3924520629971209*I} {2185, 6.882126*^-6 - 2.779896*^-6*I, 2185, 3.9373000660359043 - 1.3884205673991643*I} {2186, 6.868314*^-6 - 2.801973*^-6*I, 2186, 3.9326824194240966 - 1.388919271367764*I} {2187, 6.834397*^-6 - 2.821619*^-6*I, 2187, 3.9193119034091612 - 1.392129629340478*I} {2188, 6.8773*^-6 - 2.810891*^-6*I, 2188, 3.944978491530118 - 1.390943263955661*I} {2189, 6.848299*^-6 - 2.808148*^-6*I, 2189, 3.94098128090196 - 1.3901191519414469*I} {2190, 6.855072*^-6 - 2.790443*^-6*I, 2190, 3.949994462885084 - 1.3839727133323532*I} {2191, 6.859579*^-6 - 2.803622*^-6*I, 2191, 3.9613958922798744 - 1.3886625790012508*I} {2192, 6.863593*^-6 - 2.805449*^-6*I, 2192, 3.959620068764269 - 1.3999689844583947*I} {2193, 6.828402*^-6 - 2.806046*^-6*I, 2193, 3.9450691063244445 - 1.3986825622097558*I} {2194, 6.855874*^-6 - 2.763078*^-6*I, 2194, 3.985336820009134 - 1.3753841792920498*I} {2195, 6.852584*^-6 - 2.79741*^-6*I, 2195, 3.9706648245292793 - 1.3968104984348502*I} {2196, 6.847968*^-6 - 2.801543*^-6*I, 2196, 3.970896877023106 - 1.4052347070913531*I} {2197, 6.857821*^-6 - 2.804837*^-6*I, 2197, 3.9836526206298215 - 1.414877382260006*I} {2198, 6.84141*^-6 - 2.80289*^-6*I, 2198, 3.9804711974669233 - 1.4124399412668391*I} {2199, 6.823047*^-6 - 2.795037*^-6*I, 2199, 3.983906643421614 - 1.4067204836782592*I} {2200, 6.839617*^-6 - 2.802913*^-6*I, 2200, 3.9964841558060007 - 1.4173287152772052*I} {2201, 6.84435*^-6 - 2.796775*^-6*I, 2201, 4.006054552240088 - 1.4192435661320537*I} {2202, 6.819622*^-6 - 2.791963*^-6*I, 2202, 4.003780880566996 - 1.4174223698519708*I} {2203, 6.83232*^-6 - 2.78467*^-6*I, 2203, 4.016825479170927 - 1.420928741358091*I} {2204, 6.836337*^-6 - 2.787057*^-6*I, 2204, 4.0198412253199285 - 1.42050804280531*I} {2205, 6.819138*^-6 - 2.80714*^-6*I, 2205, 4.00914942751822 - 1.4238523116602857*I} {2206, 6.83031*^-6 - 2.80324*^-6*I, 2206, 4.023807549837072 - 1.4209612361108226*I} {2207, 6.818188*^-6 - 2.789735*^-6*I, 2207, 4.024859811592211 - 1.420111265173186*I} {2208, 6.805907*^-6 - 2.813099*^-6*I, 2208, 4.019525560121129 - 1.434235289775516*I} {2209, 6.82952*^-6 - 2.797539*^-6*I, 2209, 4.039670085348632 - 1.4365589722645464*I} {2210, 6.808193*^-6 - 2.791215*^-6*I, 2210, 4.03770349223736 - 1.433726742305237*I} {2211, 6.800515*^-6 - 2.788515*^-6*I, 2211, 4.039830121301563 - 1.4319117438824804*I} {2212, 6.790083*^-6 - 2.810558*^-6*I, 2212, 4.034187249574324 - 1.4351716583602154*I} {2213, 6.81026*^-6 - 2.785854*^-6*I, 2213, 4.050581026306178 - 1.4319767215542865*I} {2214, 6.795889*^-6 - 2.788577*^-6*I, 2214, 4.055248534445954 - 1.4315452751309263*I} {2215, 6.787545*^-6 - 2.799883*^-6*I, 2215, 4.052586497463547 - 1.4350752939655496*I} {2216, 6.799948*^-6 - 2.791731*^-6*I, 2216, 4.05760673220008 - 1.4389866424404933*I} {2217, 6.795038*^-6 - 2.787931*^-6*I, 2217, 4.060628363622717 - 1.4428625446663315*I} {2218, 6.787343*^-6 - 2.787471*^-6*I, 2218, 4.0621038047698566 - 1.4416249141529123*I} {2219, 6.783163*^-6 - 2.783544*^-6*I, 2219, 4.075113809319525 - 1.438000793925118*I} {2220, 6.783978*^-6 - 2.805244*^-6*I, 2220, 4.074269184958854 - 1.4576539151258918*I} {2221, 6.793796*^-6 - 2.785501*^-6*I, 2221, 4.078579223588714 - 1.463240185192152*I} {2222, 6.787337*^-6 - 2.784189*^-6*I, 2222, 4.0834955559668815 - 1.4573921938040215*I} {2223, 6.779918*^-6 - 2.783548*^-6*I, 2223, 4.092503946911323 - 1.4573471715624076*I} {2224, 6.776735*^-6 - 2.78048*^-6*I, 2224, 4.095792565116663 - 1.4588333386142454*I} {2225, 6.777195*^-6 - 2.787716*^-6*I, 2225, 4.0983957754839935 - 1.4641114515719134*I} {2226, 6.775281*^-6 - 2.790124*^-6*I, 2226, 4.104015661844455 - 1.4656477124478113*I} {2227, 6.773101*^-6 - 2.785264*^-6*I, 2227, 4.107525162565304 - 1.4684979850068935*I} {2228, 6.766743*^-6 - 2.791159*^-6*I, 2228, 4.104800791203747 - 1.4714664145975693*I} {2229, 6.761579*^-6 - 2.793858*^-6*I, 2229, 4.10739611952681 - 1.466780889186022*I} {2230, 6.753926*^-6 - 2.789418*^-6*I, 2230, 4.111392265229108 - 1.461310308151179*I} {2231, 6.766363*^-6 - 2.784595*^-6*I, 2231, 4.123197058572322 - 1.4793569788317027*I} {2232, 6.763234*^-6 - 2.78709*^-6*I, 2232, 4.125996271692607 - 1.4859857151717981*I} {2233, 6.767477*^-6 - 2.781558*^-6*I, 2233, 4.136415524010027 - 1.4854107214429337*I} {2234, 6.7617*^-6 - 2.778192*^-6*I, 2234, 4.138826308769239 - 1.4836223200876804*I} {2235, 6.750911*^-6 - 2.776353*^-6*I, 2235, 4.138252192460567 - 1.4836229920103567*I} {2236, 6.74947*^-6 - 2.799801*^-6*I, 2236, 4.14146069480474 - 1.488783833619798*I} {2237, 6.763321*^-6 - 2.783349*^-6*I, 2237, 4.152343284125318 - 1.4885772356279452*I} {2238, 6.741554*^-6 - 2.782332*^-6*I, 2238, 4.150458618974985 - 1.487197359612043*I} {2239, 6.745107*^-6 - 2.790197*^-6*I, 2239, 4.156180694959422 - 1.4933069192649575*I} {2240, 6.743213*^-6 - 2.772741*^-6*I, 2240, 4.161974050600797 - 1.4832022796213584*I} {2241, 6.740793*^-6 - 2.782585*^-6*I, 2241, 4.16638852874923 - 1.4900489334909475*I} {2242, 6.72468*^-6 - 2.778625*^-6*I, 2242, 4.164186489338492 - 1.4882354350674727*I} {2243, 6.718033*^-6 - 2.783511*^-6*I, 2243, 4.16318835877156 - 1.4929024532106245*I} {2244, 6.7174*^-6 - 2.770264*^-6*I, 2244, 4.174742712717295 - 1.4872113330650936*I} {2245, 6.740613*^-6 - 2.772061*^-6*I, 2245, 4.19012952038036 - 1.506858660864479*I} {2246, 6.751633*^-6 - 2.771934*^-6*I, 2246, 4.194846246017292 - 1.5111565602692*I} {2247, 6.731341*^-6 - 2.777695*^-6*I, 2247, 4.188768912544396 - 1.5069438331202023*I} {2248, 6.722058*^-6 - 2.770785*^-6*I, 2248, 4.188363902885949 - 1.5042588932749437*I} {2249, 6.711529*^-6 - 2.774349*^-6*I, 2249, 4.186792453669147 - 1.5057550884242406*I} {2250, 6.721184*^-6 - 2.775183*^-6*I, 2250, 4.190838381887657 - 1.514715220640729*I} {2251, 6.724209*^-6 - 2.749935*^-6*I, 2251, 4.206280066797575 - 1.5008837931882573*I} {2252, 6.717107*^-6 - 2.774828*^-6*I, 2252, 4.2049224525718145 - 1.5146759276496642*I} {2253, 6.717043*^-6 - 2.780137*^-6*I, 2253, 4.208095108105739 - 1.5217686092879978*I} {2254, 6.695344*^-6 - 2.785387*^-6*I, 2254, 4.200847907211598 - 1.5254633170842102*I} {2255, 6.711527*^-6 - 2.763277*^-6*I, 2255, 4.220087216360429 - 1.5133370247020097*I} {2256, 6.713857*^-6 - 2.763101*^-6*I, 2256, 4.232203454501219 - 1.5215534628186256*I} {2257, 6.711253*^-6 - 2.773469*^-6*I, 2257, 4.228381625132814 - 1.5281394857952872*I} {2258, 6.696277*^-6 - 2.772307*^-6*I, 2258, 4.2257983225434606 - 1.5279337348891038*I} {2259, 6.704867*^-6 - 2.766645*^-6*I, 2259, 4.234610739095543 - 1.5312801323371372*I} {2260, 6.694108*^-6 - 2.77166*^-6*I, 2260, 4.233119203814173 - 1.5331285283242204*I} {2261, 6.708348*^-6 - 2.766155*^-6*I, 2261, 4.244690284894718 - 1.5408468807158584*I} {2262, 6.689907*^-6 - 2.76961*^-6*I, 2262, 4.2403399700552304 - 1.5369970223778653*I} {2263, 6.703277*^-6 - 2.77298*^-6*I, 2263, 4.251949179483417 - 1.5454535036827153*I} {2264, 6.690236*^-6 - 2.770264*^-6*I, 2264, 4.249841558623808 - 1.5422903230297549*I} {2265, 6.67901*^-6 - 2.770875*^-6*I, 2265, 4.248721976784826 - 1.5403416904074612*I} {2266, 6.69454*^-6 - 2.793665*^-6*I, 2266, 4.248642205793574 - 1.5658273523686004*I} {2267, 6.700744*^-6 - 2.772985*^-6*I, 2267, 4.26897559818285 - 1.5619971346491237*I} {2268, 6.695057*^-6 - 2.768057*^-6*I, 2268, 4.27172528200214 - 1.5584389979012006*I} {2269, 6.674114*^-6 - 2.773024*^-6*I, 2269, 4.2633349688449815 - 1.5589723030819618*I} {2270, 6.684982*^-6 - 2.774083*^-6*I, 2270, 4.27382150761007 - 1.5603399832022804*I} {2271, 6.678731*^-6 - 2.762147*^-6*I, 2271, 4.280419557954161 - 1.5534243838936832*I} {2272, 6.673638*^-6 - 2.770357*^-6*I, 2272, 4.284310780235642 - 1.55702460224586*I} {2273, 6.672943*^-6 - 2.761816*^-6*I, 2273, 4.282706737479944 - 1.5602426333965849*I} {2274, 6.681989*^-6 - 2.763845*^-6*I, 2274, 4.292261442069972 - 1.5674717757100687*I} {2275, 6.664019*^-6 - 2.76305*^-6*I, 2275, 4.289525003433312 - 1.5665137624286536*I} {2276, 6.664885*^-6 - 2.751161*^-6*I, 2276, 4.29658568949003 - 1.5658103955019804*I} {2277, 6.669658*^-6 - 2.771221*^-6*I, 2277, 4.302758565183426 - 1.5716029842730743*I} {2278, 6.659953*^-6 - 2.769548*^-6*I, 2278, 4.299720348925066 - 1.5694624795675125*I} {2279, 6.661438*^-6 - 2.767906*^-6*I, 2279, 4.3020003101762505 - 1.5746586054747325*I} {2280, 6.666541*^-6 - 2.760089*^-6*I, 2280, 4.311206423164673 - 1.580451000590625*I} {2281, 6.655712*^-6 - 2.770936*^-6*I, 2281, 4.310867503957515 - 1.5824622146961864*I} {2282, 6.656323*^-6 - 2.774936*^-6*I, 2282, 4.314932781453278 - 1.5903116645458195*I} {2283, 6.662137*^-6 - 2.774621*^-6*I, 2283, 4.323217952523653 - 1.5945131766777614*I} {2284, 6.643218*^-6 - 2.766448*^-6*I, 2284, 4.319494577207611 - 1.5837881485004612*I} {2285, 6.651096*^-6 - 2.782457*^-6*I, 2285, 4.322865817556966 - 1.596473178884098*I} {2286, 6.655947*^-6 - 2.762655*^-6*I, 2286, 4.3352181160445475 - 1.5962652890178826*I} {2287, 6.640707*^-6 - 2.762674*^-6*I, 2287, 4.329885216885837 - 1.5961259547310138*I} {2288, 6.637211*^-6 - 2.758068*^-6*I, 2288, 4.329693211437779 - 1.5974528852438767*I} {2289, 6.642827*^-6 - 2.7715*^-6*I, 2289, 4.332188811188651 - 1.6062470082170501*I} {2290, 6.654866*^-6 - 2.771188*^-6*I, 2290, 4.354415953754533 - 1.6105589340267878*I} {2291, 6.639392*^-6 - 2.767705*^-6*I, 2291, 4.349021201714618 - 1.602048370196409*I} {2292, 6.645909*^-6 - 2.767249*^-6*I, 2292, 4.352146178120732 - 1.609158794876874*I} {2293, 6.62729*^-6 - 2.767888*^-6*I, 2293, 4.347820034737213 - 1.6094762533624545*I} {2294, 6.637962*^-6 - 2.768225*^-6*I, 2294, 4.356417556669164 - 1.6184425058801577*I} {2295, 6.628591*^-6 - 2.756928*^-6*I, 2295, 4.361963079849834 - 1.61315331012612*I} {2296, 6.628921*^-6 - 2.766534*^-6*I, 2296, 4.364460420474859 - 1.6217518502580535*I} {2297, 6.63498*^-6 - 2.761168*^-6*I, 2297, 4.371335945931907 - 1.6253843162337194*I} {2298, 6.63299*^-6 - 2.777514*^-6*I, 2298, 4.366746667262532 - 1.6355303034492967*I} {2299, 6.632453*^-6 - 2.754843*^-6*I, 2299, 4.3783814736563755 - 1.6192411379860745*I} {2300, 6.61952*^-6 - 2.753013*^-6*I, 2300, 4.379893619939514 - 1.6209951415175987*I}

Where the 1000, 1001,.. are f (independent) and the first complex "KompM" and the second "Rho".

• I suggest that you simplify your problem, for example using only a few data points. Short, precise questions are more likely to get useful answers. – mikado Jul 2 '17 at 5:45
• Your list of data at the end is not a proper list in that it lacks separating commas. It would be better if you can provide it as a code block including the complete input with the commas. Generally speaking this is not too difficult to do; you can split the data and model into real and imaginary parts and fit to them both simultaneously. There are lots of questions about simultaneous fitting on the site. – Oleksandr R. Jul 2 '17 at 11:49