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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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What's a complex number? | Comment 9 of 19 |
A complex number is said to have the form a+bi. One solution here uses a number in which a is zero, making the number purely imaginary. If b were zero it would be purely real. Is the purely imaginary number considered complex, even though the purely real number is not?
  Posted by Charlie on 2003-11-26 08:11:21
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