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I'm learning Complex Numbers by myself. I've already understood basics concepts, but now I have problems with plots/graphs.

For example, I don't know, how to plot:
(1) $|z-1|+|z+1|=4$

(2) $|z+1| - \Im z \leq 1$

(3) $\Re\left(\frac{1-z}{1+z}\right) = 1$

($z \in \mathbb{C}$)

These examples are from some problem set I'm learning from (it's for first year college students)

I would really appreciate your help. I don't want to get answers for these particular problems. I want to understand, how can I plot similar things.

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    Take z=x+iy and redice the equations in complex variables to an equation in $x,y\in\mathcal{R}$ Notice that all the operations in your question return real arguments (Re, modulus, Im, etc)2011-03-20

2 Answers 2