Question: Converting cartesian coordinates on a circle to polar form

Suppose you have some functions like:

S^1 --> S^1: w(x,y) = (x^2 - y^2, 2xy)

Then this is equivalent of

w(exp(i 2Pi t)) = exp(i 4 Pi t)

Or if I have S^1 --> S^1: w(x,y) = (-y,x), we would get:

w(exp(i 2Pi t)) = exp(i 2 Pi (t+1/4))


How can I obtain the second form of the expression in Maple given the first one?

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