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Math Help - Euler's Formula

  1. #1
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    Euler's Formula

    I am having trouble understanding how somethign came up, I am sure it's something stupid that I just can't notice right now but I will ask anyway.

    So to derive the cos (x+y) and sin(x+y) identities we write
    <br />
e^{ix}e^{iy} = (cosx + isinx)(cosy +isiny)
    = cosxcosy + isinxcosy + isinycosx - sinxsiny
    = cosxcosy - sinxsiny + i(sinxcosy + sinycosx)

    Therefore, cos(x+y) = cosxcosy - sinxsiny
    sin(x+y) = sinxcosy + sinycosx
    However, I do not understand the bolded part because I am thinking that (isinx)(isiny) would = isinxisiny. So how did we get the negative sign and the elimination of the i's?
    Last edited by sazafraz; September 7th 2008 at 05:13 AM.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by sazafraz View Post
    So how did we get the negative sign and the elimination of the i's?
    The reason is that i^2=-1.
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  3. #3
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    Quote Originally Posted by flyingsquirrel View Post
    Hi,

    The reason is that i^2=-1.
    oh ok thank you, I didn't know that i is an imaginary unit
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