Prove that if all of the powers invoved are principal values then...
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We can write:
(1/z)^c= (1/r)^(c)*exp(-i*c*theta))= r^(-c)*exp(-i*c*theta)= [r*exp(i*theta)]^(-c)= z^(-c)
Note that we are considering the principal value, so we do not have to worry about c.
A Principal Value Proof is provided.