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Math Help - Can you raise stuff to the power of "i" ?

  1. #1
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    Can you raise stuff to the power of "i" ?

    Can you raise variables to the power of "i"--the imaginary unit--just as you would raise them to the power of a real number?

    For example, can I take this equation...

    1=ax^{2}

    ...and do this...

    1^i=(ax^{2})^i

    ...resulting in...

    1=a^i x^{2i}

    Or is that against the rules?
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  2. #2
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    You can raise any number to any power you like, but you should convert everything to exponential polar form, makes exponentiation much easier...

    E.g. 1^i = (1 + 0i)^i

     = (\cos{2\pi n} + i\sin{2\pi n})^i, where n is an integer

     = (e^{2\pi n i})^i

     = e^{2\pi n i^2}

     = e^{-2\pi n}.
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