Questions tagged [complex]

Questions about using complex numbers in Mathematica. This includes basic arithmetic, functions of complex numbers, plotting complex functions, and dealing with branch cuts.

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2
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1answer
117 views

How do I draw a conformal mapping from the z-plane to the w-plane

I am total beginner in Mathematica. Don't know a thing. I need to draw some diagrams for showing the conformal nature of map $w=e^z$. I need to draw some contours in $z$-plane; e.g., horizontal line, ...
0
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0answers
30 views

Matrix formed with ConjugateTranspose not in form I want [closed]

I am trying to calculate the matrix multiplication and then take its conjugate transpose. But the problem is when I use ConjugateTranspose, it gives me a matrix ...
0
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0answers
61 views

How to find all numerical complex roots of a non-algebraic function?

The problem arises from solving non-algebraic equation, say I have a equation $x e^x =1$, every body knows that its solution is Lambert function with an integer indices, i.e. $W_k(1)$ , where $k\in\...
5
votes
1answer
100 views

Keeping Phase Factors in Sqrt

I am trying to plot certain holomorphic functions that contain square and higher roots. In the complex analysis sense, the function $f:z\mapsto z^\alpha$ for some $\alpha\in\mathbb C$ has a phase ...
3
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2answers
132 views

Complex Data Fitting

I have a complex data set and I want to fit with a mathematical model using NonlinearModelFit, but an error appears. Following is the data I'm using and the code ...
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2answers
91 views

How to get F from this transcendental complex equation?

I want to solve this transcendental equation, but I don't know the step by step to get F in form equation and value of F ...
4
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2answers
109 views

How to factor a polynomial expression with variable coefficients (and imaginary values)

How can I factor terms with variable coefficients? For example for the expression: $x^2 + a$ I know that I can factor this to: $(x+i\sqrt{a})(x -i\sqrt{a})$ How do I do this in mathematica? I would'...
1
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1answer
58 views

Add vertical lines to `ComplexPlot3D` at roots

I have a Table of 6 plots of polynomials of increasing degree, using ComplexPlot3D: ...
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0answers
97 views

Incorrect results from FunctionAnalytic [duplicate]

Investigating a new command of version 12.2 FunctionAnalytic, I detect that the command badly works with Re an ...
3
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1answer
173 views

Incorrect answer of FunctionAnalytic

A new command FunctionAnalytic of version 12.2 sometimes produces incorrect results, e.g. FunctionAnalytic[Cos[Sqrt[z]], z] <...
0
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1answer
73 views

Solve complex heat transfer equation

I am trying to solve a heat transfer problem related to calculating the cooling rate after quenching a sample. The equations (and explanations) are taken from this paper: https://sci-hub.se/10.1029/...
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1answer
38 views

Conjugating the following function

I want to conjugate the above function. It's not working using the below code. Please help. All variables are real and greater than zero. ...
1
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1answer
48 views

I have a function $R \to C$, I want to plot it as the way we can plot parametric equations in the $R^2$. How to do it?

I have a real variable $t$ and a function $f(t)$ giving complex values. How to plot the function for $t$ in a given real interval? Also is there a way to do it in Wolfram Alpha website?
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2answers
69 views

Problem with integral of the type (x^2-y^2)^a/2 x^2 Exp[-x]

I tried to calculate the following integral using Mathematica Integrate[(x^2 - y^2)^(3)/2 x^2 Exp[-x], {x, y, Infinity}] The answer was a conditional expression ...
2
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0answers
43 views

How to numerically solve ODEs with a complex variable?

I want to solve the following ODEs: 3(a'[z])^2 == 1/2 a[z]^2 (p'[z])^2 - 1 ; a[z]p''[z] + 3a'[z]p'[z] + z^2 == 0 ; where z is ...
1
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1answer
31 views

How to find the norm of an imaginary exponential expresion?

I need to find the norm of the following expression $$ |1+e^{-i2\pi w}+e^{-i4\pi w}|^2$$ With w real number. For doing this I coded: ...
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0answers
43 views

Do these solutions actually amount to a solution over the Reals and not over the Complexes as Mathematica says?

The following program outputs approximations to ZetaZero[1] and ZetaZero[-1]: ...
1
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1answer
45 views

Understanding and visualizing Bessel function with complex argument

I have a vector field in polar coordinates $(r,\phi)$, which I wish to visualize and better understand. It represents the Electric field vectors for a given field distribution inside a circular ...
1
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2answers
32 views

How to help Simplify with conjugates without using ComplexExpand

I have a seemingly simple simplification involving conjugates: $Assumptions = Element[{a}, Reals]; FullSimplify[ x E^(I a) + Conjugate[x] E^(-I a)] which merely ...
2
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0answers
26 views

NMinimize to ignore arguments for which function is complex valued [closed]

I'd like to minimize a pretty complicated function $f(x, y, z)$ with NMinimize, however for certain values of the arguments $f$ becomes complex valued, and my ...
1
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1answer
41 views

How do I find the maximum of a certain complex expression? [closed]

I have this expression: TFilter1 = -(7.5438*10^8/(6.34731*10^8 + 48270.2 s + s^2)) where s is a complex variable give by $s = ...
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0answers
22 views

Can't plot derivative of Hankel function [duplicate]

I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...
4
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3answers
120 views

Plot a set of complex numbers with given argument and absolute value bounds

I want to plot the following complex numbers $$z \in \text{(complex numbers)}:\pi/4 < \arg (z) \leq 5 \pi/4,\ 1 \leq |z| < 2 $$ I don't know how to graph it so that it would look like 2D without ...
2
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0answers
38 views

Verifying Gram-Schmidt Algorithm with Mathematica [closed]

According to a review of the Graham-Schmidt alogirithm in my textbook: This is only the first part of the procedure, but it's what I'm focused on for this post. I attempted to verify that $\langle 1 ...
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3answers
49 views

Solving equations with complex or real or imaginary number

GG = {N3*Conjugate[N3]+ N4*Conjugate[N4] == 1, (2 N3 + (-I + Sqrt[2]) N4)/(2 Sqrt[3]) == 0}; Sols = Solve[GG, {N3, N4}] I need to solve the above equation. But I ...
2
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1answer
76 views

Complex Solutions not in a+bi form

Solve[x^2 + x + 1 == 0, x] gives the solution: {{x -> -(-1)^(1/3)}, {x -> (-1)^(2/3)}} I know these are complex solutions but I'd like to have them in a+bi form. If I do N@Solve...I get the ...
1
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2answers
107 views

ParametricPlot3D as a ContourPlot

I want to plot the amplitude of a complex-valued function of one complex variable. I want to do this in the plane defined by the real and imaginary parts of the complex variable as a ...
4
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1answer
72 views

Plotting a hexagonal histogram

For positive integers $D$, I have a function s[D_] which creates a list of complex numbers, all of the form $a+b\sqrt{-D}$, where $a$ and $b$ are integers. These ...
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0answers
61 views

Problematic matrix calculation [closed]

I have defined matrix as such u1 = {0, I, 0, 1}; u2 = {I, 0, 1, 0}; λ1 = Sqrt[m/2] (u1 + (I*u2)); Now I define the matrix multiplication with $ 4\times 4 $ matrix ...
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2answers
34 views

Plotting partial sum with complex number

$$\sum_{n=1}^{N} e^{2\pi in\sqrt2}$$ We have to use Accumulate and ListLinePlot, and my implementation so far with upper bound ...
1
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1answer
34 views

How to check if a complex number belongs to a quadratic field

I am working with lists of complex numbers and want to be able to determine which out of these lists contains only elements from a certain quadratic field, $\mathbb{Q}(\sqrt D) = \{ a+b\sqrt D :a,b \...
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0answers
31 views

Abs function for complicated complex arguments [closed]

I want to find the Abs square of this complex expression. I tried using Abs command and then squaring it but nothing happened, it just showed 'Abs' in the output. I also tried multiplying it with its ...
1
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2answers
68 views

Is there some way I can do integrations on the complex plane without converting it to real and imaginary parts by hand?

For example how do I actually write this in Mathematica? Integrate[ 1/(z^2+1/4), "z on the Unit Circle with origin as center" ]
3
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1answer
85 views

Missing roots/contours in ContourPlot

I have read some similar equations in other places, but it seems like theirs suggestions does not work in my case. I would like to plot a complex equation in complex plane by the ContourPlot, the ...
0
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1answer
82 views

Why does this integral of a real, analytic, absolutely integrable function give a complex result?

I am using Mathematica to develop some ``interesting" problems for students to solve using Fourier series. The following computation seems as though it should yield a real result: $B_n = \int_0^1 ...
2
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3answers
113 views

Best way to solve for domain on which a function is real

Say I have a function like ...
0
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3answers
37 views

How to specify domain? [closed]

I wrote x $\in$ Reals; y$\in$ Reals; z = x + I y; Re[z] gave the output -Im[y] + Re[x] as if the first line did not exist How can I specify that x and y are reals?
0
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0answers
42 views

Solve a system of complex equations and plot the solution

I'm trying to solve a system of 2 equations with an unknown real parameter k0, the solution is complex. then I want to plot the obtained solution function of k0: here is my code: (I here is the ...
2
votes
3answers
135 views

Plotting Minkowski product of two sets in complex 2D plane

I am trying to draw Minkowski product of two sets in complex 2D plane in Mathematica. While I can draw the individual complex 2d plane for these sets in Mathematica ...
0
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0answers
39 views

Complex mapping of curve

I have a curve in the complex plane (a unit circle), and I want to plot the curve with a complex function applied to it ($f(z)=\sqrt{z}$) How do I go about doing that? I know how this can be done ...
14
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1answer
178 views

Why does Abs return negative values?

According to the documentation Abs[z] gives the absolute value of the real or complex number z and is also known as the modulus. As far as I'm aware for any definition of the absolute value, norm or ...
3
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1answer
33 views

Stopping Simplify and FullSimplify expressing real terms as complex

I am working with real functions but FullSimplify and Simplify express them as complex terms. I assume this is because the ...
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0answers
63 views

Why does Log[Abs[#]] return a complex number?

For a nonzero number $x$, $\log|x|$ should be a real number. Why does the following NestList contain non-real numbers when no numbers involved are close to zero? Is it a bug? ...
2
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1answer
49 views

Using callout[] to create a plane

I want to create a plane that represents $15$ powers of complex number: $a$1 $= (10/7)*(Cos(Pi/10) + i*Sin(Pi/10)) $. I also want to label the points with the text "a to power k" where $k$ ...
0
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1answer
46 views

Searching for elegant way manipulate complex vectors

I have some complex vectors that I would like to normalize and further manipulate. For example, one is this: ${\qquad \rm vec}=(-\frac{-a + b + \sqrt{a^2 - 2 a b + b^2 + 4 c^2 + 4 d^2}}{2 (c + i d)},1)...
1
vote
1answer
128 views

How do I visualize $\exp(z)$ as a complex mapping?

How do I visualize $\exp(z)$ as a complex mapping? How can I ensure that it does not miss any value on the complex plane as it's value (is in the best condition of Picard's theorem). Can anyone help ...
0
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1answer
89 views

non linear model fit for a complex function

I am trying to fit a complex function which is basically a function for anelastic relaxation. I have 3 columns in my dataset Data , first column is the temperature (which I have denoted by x here), ...
0
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0answers
82 views

Why does Mathematica give the wrong answer for this integral, and how can I correct it?

Mathematica is getting the following integral completely wrong: $Assumptions = a > 0; Integrate[1/k (E^-(k + a)^2 - E^-(k - a)^2), {k, 0, ∞}] (* I E^-a^2 π *) ...
0
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1answer
33 views

Complex Conjugate Help

I am trying to follow my teacher's instructions to easily compute for a complex conjugate but I get mathematica to actually reveal the complex conjugate besides the word "conjugate" and even ...
0
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0answers
45 views

Head of complex sum

We have: 1 + 2 I + 3 + 4 I // Head Complex and 1 + 2 I + 3/5 + 4/5 I // Head Complex But we get: ...

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