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I Can Euler's Identity be used?

  1. Oct 18, 2016 #1
    I have a homework question and I am wondering if you can use Eulers identity in this case.

    If the equation is f(x)=constant*e^(-x^2) can this be rewritten as f(x)=consant*e^(ix)^2
    and then, can you use the identity when it is in this form?

    Edit: Can it be put in the form cosx+isinx

    I am not well acquainted with Eulers Identity so bear with me
     
    Last edited: Oct 18, 2016
  2. jcsd
  3. Oct 18, 2016 #2

    PeroK

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    What do you propose to do with $${e^{(ix)}}^2$$
     
  4. Oct 18, 2016 #3
    sorry edited for clarity
     
  5. Oct 18, 2016 #4

    PeroK

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    Sadly ##exp((ix)^2) \ne (exp(ix))^2## if that's what you intended.
     
  6. Oct 18, 2016 #5

    mfb

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    You can use ##\exp(-x^2) = \exp(i (ix^2))## and use the Euler formula for that expression, but that gives imaginary arguments for the sine and cosine, which does not look helpful.
     
  7. Oct 18, 2016 #6

    mathman

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    There is an equivalent formula involving sinh and cosh, but I doubt if it would help you.
     
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