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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How to extract only real solutions from the result of Solve

For Example, I have the following polynomial equations: $$ \left\{ \begin{array}{ll} \dfrac{2025 (208 x+5 (y-3446))}{52 (y+90)^2}+\dfrac{300 (8 x-21 y+1920) (y-80)}{7 (x+30)^3}+\frac{300 (80 x-21 z+...
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2answers
1k views

Why doesn't FullSimplify drop the Re function from an expression known to be real?

For some reason Mathematica does not properly simplify this expression: ...
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1answer
125 views

Using NSolve for Elliptic Equations over Fundamental Parallelogram in Complex Plane

I'm considering solving elliptic functions over a fundamental domain of the torus with half-periods $\omega_{1}=\pi/2$ and $\omega_{2} = \pi \tau /2$, where $\tau$ is the modular parameter of the ...
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0answers
37 views

Pole expansion with complex roots

I have the following function of ω ...
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0answers
36 views

Inconsistent pole/roots decomposition

I have the following function f of ω: ...
5
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0answers
159 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
2
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2answers
118 views

Plot3D in a loop for Riemann surfaces of the nth-root

I would like to plot the Riemann surfaces for $n$ functions of the form: $$ > f(z) = z^{\frac{1}{n}} = (x + iy)^{\frac{1}{n}} $$ For example for the function $$ > f(z) = z^{\frac{...
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2answers
143 views

How to solve this set of equation in complex domain?

First, I got a real version of equation set Solve[{d u^2 - d v^2 == 2 e u v, (u u + v v) == 1}, {u, v}] This can be correctly solved in the blink of an eye. Now ...
6
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2answers
200 views

Series expansion gives incorrect result

Bug introduced after 10.4 and persisting through 11.3.0 Mathematica 11.1.1.0 tells me that ...
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2answers
217 views

Equivalence of ComplexExpand and assuming real arguments

I am wondering why this simplification does not work, FullSimplify[Im[1/Sin[a]], Assumptions -> Element[a, Reals]] (*Out[1]= Im(csc(a))*) while this does: <...
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0answers
50 views

Using Refine function and take real part of a symbolic expression

I am trying to take the real part of the a complex expression using Refine function. However, the result doesn't come out as expected. The final result still ...
4
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1answer
183 views

How to force a real function to appear with real components [closed]

The command Integrate oftentimes produces output that seems to be a mix of real and complex components even though the result is a real function. The question is ...
1
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1answer
239 views

How to draw Lemniscate of Bernoulli type curves for higher degree polynomials

The lemniscate of Bernoulli is a curve in the complex plane given by $|z^2-1|=1$ that has the shape of $\infty.$: This is a special case of the Cassini ovals that has the form $|z^2-1|=r^2$ for $r\in\...
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0answers
250 views

Contour integral calculation [closed]

There is an integral of a complex function to calculate: $$ \oint_{|z|=2015}\frac{3i(z^3+z-2)}{\pi(z-3)}e^{-\frac{1}{z}}dz,$$ where the contour is a circle of radius 2015. Calculating it manually I ...
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1answer
59 views

Calculus of residue

i try to do the following Assuming[k\[Element] Integers,Residue[Cos[x]/x^(k+1),{x,0}]] but any respond how to calculate for any k the k derivate of Cos function ...
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2answers
79 views

Calculus Residue 3

I try to calculate f[z_]:=1/(Cosh[Sqrt[3]\[Pi] z ]-Cos[z \[Pi] ]) Assuming[k\[Element] Integers,Residue[f[z],{z,(2 I k)/(I+Sqrt[3])}]] but the answer is 0 maybe ...
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2answers
91 views

Calculus of residues

I try to calculate the following residue ...
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1answer
48 views

Calculus residue backsustitution

I try to calculate f[z_] := Coth[z]/( E^z - 1)^1 and calculate ...
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2answers
92 views

Calculus Residue

How to get the following result Table[Residue[Pi F[z] Sec[Pi z], {z, 2k + 1/2}], {k, -1, 1}] {-F[-(3/2)], -F[1/2], -F[5/2]} but it is posible to get the ...
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2answers
76 views

Force an Im-Re separation in a complex number with parameter

I was doing a computation with Mathematica (summing a series) and a part of the result was the following: $$\frac{\Gamma \left(\frac{1}{4}\right)}{3 \sqrt{2} \sqrt[4]{-\frac{\sqrt[3]{r^3}}{2}-\frac{1}...
6
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2answers
343 views

How to solve this trigonometric complex ODE system?

The system of nonlinear ODE is $$ \mathrm{i}\,s(\ddot p-\frac{1}{2}\sin{2p}\;\dot q^2)=\mathrm{i}\,c\sin p\;\dot q-a\sin p+b\cos p\cos q\,,\\ \mathrm{i}\,s(\sin^2p\;\ddot q+\sin{2p}\;\dot p\dot q)=-\...
2
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2answers
91 views

How to avoid problems with the large imaginary part of LegendreQ?

I am trying to evaluate sums involving LegendreQ[n,x], the n-th order Legendre function of the second kind $Q_n(x)$, at large $x>1$. However, the problem is that ...
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1answer
162 views

The inverse Laplace Transform of a real proper rational function must be real

How does one get Mathematica to return a real answer when using InverseLaplaceTransform? Tried using Re and ...
2
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2answers
49 views

behavior of functions with parameters inside arguments

I don't understand this behavior: why does Limit[z/(z - a), z -> 0] give zero and not a condition depending on a, provided it ...
6
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3answers
621 views

Can Mathematica automatically calculate and sum over residues at all poles of a (rational) function?

The title basically says it all: is there a way in Mathematica to automatically compute the residues at all poles of a function $f(z)$ and present them as well as their sum in a list or table? A ...
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1answer
196 views

Problem in computing residue

I need to integrate the following function $F(y)$ of complex variable $y$ over the unit circle $|y|=1$: ...
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0answers
51 views

multiple residue using nest

Is there a simple way to define a multi-dimensional residue computation starting from Residue function? This should be used within a function where the number of ...
7
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3answers
565 views

Getting Arg[z] to go from $0$ to $2\pi$

I'm defining branch cut functions, and I'm using $\arg(z)$ as a building block. So I just spent an hour at the whiteboard assuming that $\arg(z)$ goes from $0$ to $2\pi$, and then I implement the code,...
2
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1answer
60 views

Make ConjugateTranspose distributive

Related to 123974, is there a way to make the ConjugateTranspose function, input as esc-hc-esc distributive for all symbols? For ...
3
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1answer
2k views

How to plot a complex functions

I am new to mathematica. I am trying to plot a complex function, though my function is complicated one I am trying to start from a basic one. Suppose I have a function ...
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0answers
44 views

paraconjugate of polynomial

I'm trying to obtain the paraconjugate of a polynomial with the following code, ...
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0answers
66 views

How do I simplify complex integer powers of 1?

In mathematica 4, when I enter FullSimplify[(-1)^n + (-1)^{3n}, n ∈ Integers], I get the desired result 2(-1)^n. ...
0
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1answer
63 views

Derivatives with respect to the independent variables $z\in\mathbb C$ and $\bar z$ [duplicate]

I want to be able to treat $z$ and its complex conjugate as independent variables, so that for instance $\partial (z\bar\,z)/\partial z = \bar z$. When I try to do this by evaluating ...
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1answer
135 views

How to solve a complex valued equation?

How can I solve $-2K\alpha^2\alpha^*+2\epsilon\alpha^*-i\frac{\kappa}{2}\alpha=0$ for $\alpha$? The solution is supposed to be $\alpha=0$ and $\alpha=r_0e^{i\theta_0}$, where $r_0=\Big(\frac{4\...
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2answers
142 views

Improper ParametricPlot3D result when using certain complex numbers

Bug introduced in 8 or earlier and persisting in 11.1 This is more out of curiosity than for any project that I'm working on. I was experimenting with the ParametricPlot3D and put in the following ...
1
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2answers
257 views

Having problems integrating a function of a complex variable [closed]

I've tried to calculate the integral And I got the result $16i \pi ^3$. I wanted to check my calculation, so I ran this code in Mathematica: ...
2
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0answers
127 views

Integral on unit disk of a function with two singularities

The goal is to prove, using Mathematica, that for $\mathbb{D}$ the unit disk and $u,v \in \mathbb{D}$, $u \neq v$, $$\frac{1}{\pi} \int_{\mathbb{D}} \frac{\mathrm{d}^2z}{(z-u)\overline{(z-v)}} = \ln(1-...
1
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1answer
150 views

How to combine regions of two 3D plots

I need to combine two plots like this Combining two plots which are in two regions but in 3D case. The problem is that I don't know where exactly boundary passes. I have two complex functions qpC32 ...
6
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2answers
586 views

Simplify — is this simplest result Mathematica can provide? [duplicate]

I have a question about Simplify: When I do a simplification the returned result is not as simple as I want. When I ask for the Norm of an complex expression, ...
1
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1answer
72 views

Trouble getting Mathematica to assume some parameters are real and simplify the expression [duplicate]

Say I enter the following code: FullSimplify[Im[r*Exp[I*theta]^2 + (s + I*t)*Exp[I*theta]], Element[theta | r | s | t, Reals]] I expect to get: ...
13
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3answers
7k views

Complex number operations: telling Mathematica variables are real

I want to do Conjugate[a + b*I], but when I do that, the solution is Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
4
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3answers
2k views

Conjugating symbolic expression [duplicate]

I am trying to conjugate a symbolic expression, and I have explicitly stated the real terms. However, I simply can't get it to work: ...
2
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2answers
352 views

Simplify an expression with complex numbers [duplicate]

How can I get a simplify expression of following when all a,b, .., f are real numbers? FullSimplify[Abs[(a+I b)+(c+I d)(e+I f)]^2]
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0answers
35 views

Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
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0answers
85 views

How to maximize the modulus of a multivariate complex-valued function?

My problem is the following. I have a messy, complex-valued function ...
0
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1answer
65 views

A better way to create list of imaginary parts of Zeta zeros

Is there a better way to create a list of the imaginary parts of Zeta zeros than Table[Im[ZetaZero[i]], {i, 1, 100}] ? For values of the index greater than a ...
0
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2answers
201 views

Simple Complex Conjugate of exponentials

Often I work with complex exponentials, and I want Mathematica to understand that the conjugate of $e^{iHt}$ is $e^{-iHt}$. Is there a simple way of doing this? Typically I use the complex-expand ...
2
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2answers
768 views

How to create InterpolatingFunction from data?

If I have a function at a number of non-uniformly spaced data points: youtReal[7.8]=2.0332;, youtReal[8.54]=6.24352354;.................. ......... and the ...
2
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1answer
116 views

How can I more efficiently define a square root with the branch cut along the positive imaginary axis?

I have a system of equations I need to solve involving square roots. I don't always have a good guess what the solutions are, and so I am fortunate that NSolve can handle these equations. I want to be ...