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The Powers that Be (Posted on 2003-11-25) Difficulty: 4 of 5
Is it possible for two complex numbers to have a real exponentiation?

In other words, if x and y are complex (each have the form a+bi), show that x^y can have a real value, or prove that it is impossible.

Note: i is the imaginary value defined as the number that yields -1 when squared. a and b are any real numbers, but b is not 0.

See The Solution Submitted by DJ    
Rating: 4.4444 (9 votes)

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Question Short solution? | Comment 1 of 19
If Z=ln(X), then X^Y = e^(Y.Z). As Y.Z can have a zero imaginary part, therefore X^Y can be real... or am I missing something?
  Posted by Federico Kereki on 2003-11-25 13:23:15
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