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Imaginary or complex powers

psi20
in Applied Mathematics

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How do those work? Like 2 to the 2i power and stuff like that. And why does it work that way?

can you word that alittle better for me,

you mean 2^2(sqrt(-1))? how much do you know in complex numbers? do you now "de moivres" theorm? conjugates etc.?

they are defined as x^y = exp{ylogx} this works for all real positive x, and can be extended with some care to all (non-zero) x.

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Like 2^i , what's that? I know about DeMoivre's Theorem and conjugates.

 

What's the exp in exp{ylogx} mean? What's it do?

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