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  1. Top | #13

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  3. Top | #14

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    !!! !!!!!!!!!!!!!!!!!!!!!!!!!!

  4. Top | #15

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    Q9)
    $ r=2 \ and \ Arg \ z=\frac{5 \pi}{3} $

    $z=2 e^\frac{5 \pi i}{3}$

    $ z^5= 2^5 e^\frac{25\pi i}{3}$

    $ z^5 = 32 \ e^\frac{ \pi i}{3}$

    $z= 16+16i\sqrt{3}$

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  6. Top | #16

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  7. Top | #17

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    \[Q5)\int cos^6xdx=\int (\frac{e^{ix}+e^{-ix}}{2})^6dx\\=\frac{1}{2^6}\int \left ( e^{6ix}+6e^{4ix}+15e^{2ix} +20+15e^{-2ix}+6e^{-4ix}+e^{-6ix}\right )dx\\=\frac{1}{2^{6}}\left ( \frac{1}{6i}e^{6ix}+\frac{3}{2i}e^{4ix}+\frac{15}{ 2}e^{2ix}+20x-\frac{15}{2}e^{-2ix} -\frac{3}{2}e^{-4ix}-\frac{1}{6i}e^{-6ix}\right )+C\\=\frac{1}{2^{5}}\left ( \frac{1}{6}sin6i+\frac{3}{2}sin4x+\frac{15}{2}sin2 x+10x \right )+C\]
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