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Math Help - The magnitude of a complex exponential

  1. #1
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    The magnitude of a complex exponential

    |e^{iwt}| = 1

    I've seen this expression a few times but without an explanation. Is the following true:

    z = re^{iwt} = r(cos(wt) + isin(wt))
    |z| = ( cos(wt)^{2} + sin(wt)^{2} )^{1/2} = (1)^{1/2} = 1

    I don't have the i included inside the square root though... Is that by convention? Because we're talking about something that's supposed to have a real value?

    Thanks for your help.
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  2. #2
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    Quote Originally Posted by director View Post
    |e^{iwt}| = 1

    I've seen this expression a few times but without an explanation. Is the following true:

    z = re^{iwt} = r(cos(wt) + isin(wt))
    |z| = ( cos(wt)^{2} + sin(wt)^{2} )^{1/2} = (1)^{1/2} = 1 Mr F says: Yes (overlooking the fact that you have an r that disappears).

    I don't have the i included inside the square root though... Is that by convention? Because we're talking about something that's supposed to have a real value?

    Thanks for your help.
    Have you studied complex numbers? If so, you should know that |a + ib| = \sqrt{a^2 + b^2}.
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  3. #3
    Junior Member slovakiamaths's Avatar
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    mod of a complex number suppose z=x+iy is equal to \sqrt{x^2+y^2}

    so |z|=\sqrt{(rcoswt)^2+(rsinwt)^2}
    |z|=r
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  4. #4
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    Thank you for the replies.
    My question about the imaginary unit was silly so please disregard.

    I figured out what I wanted.

    PS. Slovakiamaths, sorry but I don't have enough posts to reply to your PM. I'm not studying in Poland though.
    Last edited by director; May 8th 2010 at 08:28 PM.
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