# 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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### Solving equation for Complex conjugate

How to solve the equation like this: $-par-(x+yi)-a\overline{r}=0$ where $p,a,x,y$ are constant real numbers, $r$ is complex number and $\overline{r}$ is its complex conjugate. I want to solve for $r$...
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1answer
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### Numerical errors in compiled function involving real and complex numbers as output

I am trying to use the Compile command in Mathematica to reduce the computation time because of its fast execution within Mathematica and ability to use the ...
2answers
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### Comparison of Coefficients involving complex exponentials

I'm trying to solve a couple (independently) of equations of the following type $a_0 x + 3 a_1 y(1 + xe^{i3q} + e^{-iq + 2ip}) + ... = 0, \forall x, y, q, p$. Using SolveAlways doesn't work well. So ...
0answers
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### Maximize a function over complexes

Assume that I have a bounded real valued function $h(a,b)$ such that $a\in \mathbb{C}$ and $b\in [0,1]$. Can Mathematica maximize such function over $\mathbb{C}\times [0,1]$? I tried some functions ...
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### One more an incorrect result of FunctionAnalytic

Studying a new in 12.2 command FunctionAnalytic, I execute ...
1answer
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### Prove that for complex numbers you can apply the formula for the difference of squares [closed]

a^2-b^2=(a-b)(a+b) a in R, b in C
1answer
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### Principal value of a double integral numerically

I have several integrals of the form : where and . where a,b,wc and T are constants and PV denotes the Cauchy principal value I tried to integrate one of this form using NIntegrate however when ...
2answers
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### plotting the Cayley Transformation

I'm new to mathematica and I have to plot the Cayley Transformation, which maps the upper half plane to the unit disk. I want to plot the z-plane and the w-plane. I wrote this: ...
1answer
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### Visualizing convergence/divergence series

I was trying to visualize the idea of convergence/divergence of series using complex plane. I got this idea from “A First Course in Complex Analysis with Applications by Dennis Zill, Patrick Shanahan”....
1answer
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### Integral of complex function

How to compute a complicated complex integral? You can see the example in the figure. I set assumptions that all constants are positive and real, then I try to integrate the $pel(z)$ expression but ...
1answer
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### Real part of complex exponential

How do you obtain the real part of a complex exponential? For example, Mathematica gives $Re[e^{ik}]$ instead of $\cos(k)$, see figure. ...
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### How to force N[ ] to output the real value (or all values) for negative cube roots [duplicate]

Evaluating N[(-1)^(1/3)] returns 0.5 + 0.866i in my v12.0 notebook. Of course, the equation x^3 = -1 has three distinct solutions for x. Is there a global (or local) option that will force Mathematica ...
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### How to use _Complex types in CUDAFunctionLoad?

The documentation for CUDAFunctionLoad specifies various base datatypes you can use for your function's arguments, including ...