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Math Help - Complex number problem

  1. #1
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    Complex number problem

    Hey all here i m having trouble in one more question, it seems simple but i cant seem to get the desired result
    any help is greatly appreciated please

    If m = cis x & n = cis y, show that m-n/m+n = tan (x-y)/2
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Complex number problem

    If you know the exponential notation

    \dfrac{m-n}{m+n}=\dfrac{e^{ix}-e^{iy}}{e^{ix}+e^{iy}}=\dfrac{e^{i(x-y)}-1}{e^{i(x-y)}+1}=\dfrac{e^{i(x-y)/2}-e^{-i(x-y)/2}}{e^{i(x-y)/2}+e^{-i(x-y)/2}}=$\\$\ldots=i\tan\dfrac{x-y}{2}
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