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zero raised to a complex number

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0^(a+bi) 2020-12-03
From Douglas:
I realize raising 0^a = 0 if a>0 and undefined if a<=0.

If have read that 0^bi is undefined for all b.

What I don't understand is why 0^(a+bi) = 0 if a and b are not equal to zero.

Is this purely by definition or is there a logical reason why this is the case?
(I have taken Complex Analysis, so have a fairly good understanding of complex numbers.)

Answered by Penny Nom.
 
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