how he has written second term. kindly explain in steps

thanks

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- Feb 26th 2011, 11:14 PMmoonnightingalekindly explain this step of real and imaginary parts
how he has written second term. kindly explain in steps

thanks - Feb 26th 2011, 11:58 PMFernandoRevilla
Denominator:

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

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

Numerator:

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

Now, you can conclude. - Feb 27th 2011, 10:07 AMmoonnightingale
thanks