# kindly explain this step of real and imaginary parts

• February 27th 2011, 12:14 AM
moonnightingale
kindly explain this step of real and imaginary parts
how he has written second term. kindly explain in steps
thanks
• February 27th 2011, 12:58 AM
FernandoRevilla
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.
• February 27th 2011, 11:07 AM
moonnightingale
thanks