# 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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### 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
56 views

### 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. ...
0answers
17 views

### 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 ...
0answers
79 views

### How to use _Complex types in CUDAFunctionLoad?

The documentation for CUDAFunctionLoad specifies various base datatypes you can use for your function's arguments, including ...
0answers
115 views

### Does anyone have a Mathematica implementation of the standard $\arg\zeta(s)$ function required to evaluate $S(T)$?

This question is related to my question Is there an elegant exact formula for the zeta zero counting function? on Math StackExchange. Question: Does anyone have a Mathematica implementation of the ...
2answers
173 views

### How do I analytically-continue the dilogarithm function?

Here's the dilogarithm definition: $$\text{Li}_2(z)=\sum_{k=1}^{\infty} \frac{z^k}{k^2};\quad |z|<1$$ However, the function can be analytically-continued by several integral means for all $z$ with ...
1answer
86 views

### Complex exponential plot

I don't know how to plot the exponential of an imaginary number. The function I've to plot is: Exp[-I w t]. I can give w a number, so I've chose w=1 and: ...
2answers
494 views

### Simplify 1+SqrtI-Complex[1,Sqrt]

The expression 1+SqrtI-Complex[1,Sqrt] should be zero. In fact, N[1+SqrtI-Complex[1,Sqrt]] yields ...
1answer
52 views

### How to get rid of defects in that ComplexPlot3D?

I mean the result of ComplexPlot3D[Sin[z]/MittagLefflerE[10,z],{z,-1-I, 8 + I},Exclusions->None, PlotPoints -> 50] Its blow-up ...
1answer
155 views

### Formatting Imported Complex Arrays from Python (csv. files)

Just a short question, I am trying to import a complex array (matrix) from Python to Mathematica by first writing to a csv. file. When I Import the csv. array to Mathematica it is in a form (matrix ...
3answers
615 views

### How can I get the center and radius of this circle?

I am able to make Mathematica plot the solution to a complex inequality as the interior or exterior of a circle : Let $a$ be a positive real constant, and $f(z) = \frac{z+1}{z-1}$. I want to get the ...
1answer
65 views

### ComplexListPlot not complete

This code creates three complex lists. The third list is the Union of the other two. There are three plots. When applying ...
0answers
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3answers
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### Solving equations with complex or real or imaginary number

GG = {N3*Conjugate[N3]+ N4*Conjugate[N4] == 1, (2 N3 + (-I + Sqrt) N4)/(2 Sqrt) == 0}; Sols = Solve[GG, {N3, N4}] I need to solve the above equation. But I ...
3answers
144 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 ...