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We know the parametric equation of unit circle: $$\begin{cases}x=\cos(\alpha)\\ y=\sin(\alpha)\end{cases}$$ Now, let's assume $\alpha$ is complex number.

How will it look like? How to plot(visualize) it?

Edit: The range of $\alpha$ is $-5-5i$ to $5+5i$

PavelDev
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    Answers to Plotting complex numbers as an Argand Diagram discuss a more general question. Just read the answers. – Artes Apr 13 '20 at 17:11
  • @Artes I think your question is not all compatible of my question. The target of your question is visualization of complex function for some real numbers, so we have three scalars for output(complex number and input value). In my question we has four scalar for output(two complex number), therefore we are talking about four-dimensional space but I don’t know how to visualize it. – PavelDev Apr 13 '20 at 18:39
  • That isn't my question, while answers give you appropriate basis for solving your problem, at least examine my answer. Given that there is no sufficient information in your post (what subset of the complex plane is your domain i.e. where does $\alpha$ belong?) I gave just a reasonable hint. Instead of F in my answer just use Sin and Cos on appropriate curve of whatever else your domain is. Anyway my suggestion should be quite enough to figure out further steps. – Artes Apr 13 '20 at 18:57
  • @Artes I added the necessary information – PavelDev Apr 13 '20 at 19:16
  • Still not clear as it should be. If you want to visualize an image of a square domain under Cos and Sin see this post or if you want an image of a line segment under Cos and Sin then my answer is the way to go. Anyway you will not visualize a four dimensional image. – Artes Apr 13 '20 at 19:29

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