# 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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### Not getting the plot I want from ParametricPlot

1st problem My code is as follows: ...
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### 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 ...
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### Series expansion gives incorrect result

Bug introduced after 10.4 and persisting through 11.3.0 Mathematica 11.1.1.0 tells me that ...
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= Im(csc(a))*) while this does: <...
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### 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 ...
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### 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 ...
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### 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 ...
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: ...
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### 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-...
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 ...
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### 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, ...
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### 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: ...
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### 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 ...
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: ...
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### 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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### Linearity of the Conjugate operator

The output of Grad[Conjugate[x + y + z], {x, y, z}] is ...
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### How to maximize the modulus of a multivariate complex-valued function?

My problem is the following. I have a messy, complex-valued function ...
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### 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 ...
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 ...