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Math Help - need help with this equation...complex numbers??

  1. #1
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    need help with this equation...complex numbers??

    I have detached the image with the equation.
    I dont understand the steps of calculation of the H(z) equation.
    Can somebody explain how 2+2exp(j*pi/3) / (1-exp-j2*pi/3) in the numerator becomes 2exp(-j*pi*3) further down in the calculation.
    I dont see this reduction!!
    Attached Thumbnails Attached Thumbnails need help with this equation...complex numbers??-equation.jpg  
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  2. #2
    Member mohammadfawaz's Avatar
    Joined
    Feb 2010
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    Lebanon - Beirut
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    Re: need help with this equation...complex numbers??

    Well, First let's write: \frac{2+2e^{-j\pi/3}}{1-e^{-j2\pi/3}} = 2e^{-j\pi/3}.\frac{e^{j\pi/3}+1}{1-e^{-j2\pi/3}} (we just factorized 2e^{-j\pi/3} outside). Now, it remains to show that \frac{1+e^{j\pi/3}}{1-e^{-j2\pi/3}} = 1. This is easy because you should know that

    -e^{-j2\pi/3} = -(cos(-2\pi/3) + jsin(-2\pi/3)) = -cos(-2\pi/3) - jsin(-2\pi/3) = -cos(2\pi/3) + jsin(2\pi/3) = cos(\pi/3) + jsin(\pi/3) = e^{j\pi/3}

    and hence the above fractions becomes easily equal to one and therefore your result.
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