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Complex Numbers

A complex number can be represented as a pair of real numbers (cartesian coordinates)
z=x+iy or in polar coordinates z=reiϕ. The phase ϕ is defined up to a multiple of 2π

The computation of the polar coordinates is set as a problem in the list of examples.
examples

The computation of the phase ϕ requires some care:
ϕ=arctan(y/x),mod2π,forx>0
ϕ=arctan(y/x)+π,mod2π,forx<0

The case x=0 does not occure in the problem.