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Comment by NAFV_P | Hacker News Reader

  z = x + i*y = e^(a + i*b) = e^a*(e^(i*b)) = e^a(cos(b)+i*sin(b))

Both sin and cos are many to one functions. In the equation above, replacing

with

  b + 2*pi*t

where t is any positive or negative integer, would result in the same complex number.

We've used the same number for those different rotations. That does not do anything directly about irrational power p.

If p is a rational number represented by m/n, then

    360 / (m/n) * m = 360n

So there are multiples of 360 that are divisible by m/n, and we can get a unique complex number from z^p.

Now p is irrational, what happens? According to what you said, there are so many different graphs that can not be merged into just one.

EDIT: So ... we can get FINITE complex numbers (or graphs) from z^p.

Now p is irrational, what happens? According to what you said, there are infinite different graphs that can not be merged into just SOME.

I am replying to the last paragraph of darsham's comment.