# How to plot a function with complex values?

I’d like to plot a function on the complex plane, but I’m not very familiar with complex numbers in Julia anymore.

How to plot h_z(x)= e^{i \langle z,x \rangle}- 1 when z is fixed? For example, z=(1,1). How to visualize this function?

A more specific question would be, how to visualize the image of a region R = [0,1]\times [0,1], for example.

What are the best packages to implement and visualize this?

I don’t know what \langle z,x\rangle means here, but I can make a circle.

using Plots
plot(exp.(im*(0:0.001π:2π)))

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I think this problem is covered in these two posts: here and here.

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\langle z,x \rangle means inner product. In other way: z’x where x is a two-dimensional vector and ’ is the transpose operator. Remember that z is also a two-dimensional vector.