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Math Help - kindly explain this step of real and imaginary parts

  1. #1
    Member moonnightingale's Avatar
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    kindly explain this step of real and imaginary parts

    how he has written second term. kindly explain in steps
    thanks
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Denominator:

    (1-ae^{-jw})(1-ae^{jw})=1-ae^{-jw}-ae^{jw}+a^2=

    1+a^2-a(e^{-jw}+e^{jw})=1+a^2-2a\cos w\in \mathbb{R}

    Numerator:

    1-ae^{jw}=1-a(\cos w+j\sin w)=(1-a\cos w)+(-a\sin w)j

    Now, you can conclude.
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  3. #3
    Member moonnightingale's Avatar
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    thanks
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