Question

prove: if z is a complex number and 1/z=the conjugate of z over the absolute value of z squared.

Answer 1

You can write z in the form:

z = |z|exp(i theta)

Answer 2

is that how you prove it?

Answer 3

Well, if z = |z| exp(i theta), then

1/z = |z|^-1 exp(- i theta)

But z* = z exp(- i theta), so it differs by a factor 1/|z|^2