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Principal Value Proof

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Prove that if all of the powers invoved are principal values then...

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Solution Summary

A Principal Value Proof is provided.

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a)
We can write:

z=r*exp(i*theta)

1/z=1/r*exp(-i*theta) --->

(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.

b)

z=r*exp(i*theta)

z^c= ...

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