# 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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### Solution… 2nd Transcendental Equation with Graphical method [closed]

If $2x^3 + \ln x = 5$, then what is $x$? For beginning we started to find a solution for equation \begin{align}\label{eq:eq} \ln x + cx = b \tag{1} \end{align} We know from W function ...
108 views

### Replace $z z^*$ by $|z|^2$

I have a long expression involving different complex numbers. I want to force Mathematica to replace z Conjugate[z] by Abs[z]^2 ...
57 views

### Is there a function to solve a complicated event probability problem? [closed]

I need to find the probability of this beast: P[(ABEF)+(CDEH)+(ABEI)+(CDEI)+(ABEJ)+(CDEJ)]. A,B,C, etc. represent events with probabilities close to 0.5 so I don't think rare event approximation can ...
264 views

### Problem of Integrate and DSolve with inhomogeneous Legendre differential equation

I have the following inhomogeneous Legendre differential equation $(m=n=2)$: ...
34 views

### Defining 3rd variable for parametricplot3D of two-variable complex function

I am trying to make a parametricplot3D curve of the function Psi(x,t) shown in the included image. My code is the following: ...
189 views

### Portion of Curve Omitted by Plot

In the course of addressing question 104559, I encountered the following problem with Plot. Begin with ...
117 views

### How to make $\mathrm{Abs}[x + y\, I]^2$ produce $x^2 + y^2$? [duplicate]

I want to get x^2 + y^2 by evaluating Abs[a + b I]^2. Unfortunately, Mathematica just reproduces the same ...
140 views

### How to obtain left and right eigenvectors of a general complex matrix with degenerate eigenvalues?

I'm looking to obtain the left and right eigenvectors of a general complex matrix. The left eigenvectors satisfy the equation: $\phi^L_i L = \lambda_i \phi^L_i$, with $\lambda_i$ being the $i$th ...
128 views

### How to efficiently evaluate Exp[I m θ] [closed]

The I is imaginary number. My question is when m becomes large and the number of θ increases, how to evaluate it faster. Here is one way to get the result and store all the value it found. ...
227 views

### Simplify product of complex numbers

I am trying to take product of a complex number with its conjugate. When I take A*Conjugate[A] // FullSimplify The output is as desired ...
270 views

### Plot real and imaginary part of function

I have the following function: f3 = (99. (2154.43 - 100. lh^2.))/lh^1. - (0.0609773 ((2154.43 - 100.lh^2.)/lh^1.)^7.30317)/(-4.64159 - lh)^6.30317 If I plot it, ...
354 views

### Square root of complex numbers

This is a pretty simple issue with Mathematica but I could not find any previous discussion on this topic. The issue arises when we have fractions as indices of complex numbers. For e.g. Let's say we ...
157 views

### How to convert this complex number to exponential form? [closed]

I have $Z = {\frac{2+i}{2-i}}$. I need to write it in exponential form, i.e. $Z = r*e^{i{\phi}}$. I simplified the given example to ${\frac{3 + 4i}{5}}$, i.e. $a={\frac{3}{5}}, b={\frac{4}{5}}$. ...
95 views

### Solve the complex equation z^2 + ((2 + i)/5)z + 1/11 == 0 [closed]

I have tried to solve this in mathematica but cant find the right way. I used ComplexExpand[z^2 + ((2 + i)/5) z + 1/11] which gave the result ...
33 views

### Specifying different thickness for each graded contours of Mandelbrot Set so that I can export it as .STL file.

I am using Mandelbrot Set function in Mathematica to get the Mandelbrot plot. I want to 3d print this model, so want to specify thickness for each contour and then convert into .STL file. Is this ...
83 views

### Finding the real part of a complicated complex expression

I've the following code: ...
112 views

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### Why won't Mathematica Conjugate this expression>

I've been trying to replicate the derivation of Bloch's equations in Mathematica and for the final substitution, it won't correctly conjugate the expression even though I specify that all of the ...
77 views

### Why Does Mathematica Have Trouble Plotting This?

I'm trying to Plot something relatively simple: ...
90 views

### Incorrect result for the region of convergence of a simple integral

Bug persisting at least through version 11.3.0 The standard Gaussian integral Integrate[Exp[-a x^2], {x,-Infinity,Infinity}] returns ...
76 views

### General result from Integrate differs from result with special values

Can someone explain why these outputs differ? ...
81 views

### Distributing complex conjugate

If you have a statement like: Conjugate[a+b] you get back Conjugate[a+b] but I'm expecting ...
86 views

### Real integral giving complex result [duplicate]

I'm trying to calculate the following indefinite integral: $$\int \log \left(\left(\frac{\lambda ^2}{a \lambda ^2+b}+\text{\Delta 0}\right)^2\right) \, d\lambda$$ which is producing the ...
61 views

### How to create a colour picture?

Hope to have a composite colour graphics after I put in complex number, part of t=1 is a color,part of t=2 is another color,and so on. Maybe my function is not good. How to fix it? Thanks a lot! ...