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Thread: System in C

  1. #1
    Super Member dhiab's Avatar
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    System in C

    Solve in C :
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  2. #2
    MHF Contributor red_dog's Avatar
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    Replace $\displaystyle \overline{z}$ in the first equation:

    $\displaystyle iz^2=1\Rightarrow z^2=-i=\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2}$

    Then $\displaystyle z_1=\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}=i\frac{\sqrt{2}}{2}$

    $\displaystyle z_2=\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4}=\frac{\ sqrt{2}}{2}-i\frac{\sqrt{2}}{2}$
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by dhiab View Post
    Solve in C :
    let $\displaystyle z=a+ib$

    a) $\displaystyle \overline{z}z=1$

    $\displaystyle (a-ib)(a+ib)=1$

    $\displaystyle a^2+b^2=1$ ---------- (1)

    b) $\displaystyle iz=\overline{z}$

    $\displaystyle i(a+ib)=(a-ib)$

    $\displaystyle ai-b=a-ib$

    Equating real and imaginary parts, we get

    $\displaystyle a=-b$

    Substituting this in (1), we get

    $\displaystyle 2a^2=1$

    $\displaystyle a=\pm \frac{1}{\sqrt2}$

    $\displaystyle b=\mp \frac{1}{\sqrt2}$

    Hence $\displaystyle z=\frac{1}{\sqrt2}-\frac{i}{\sqrt2}$

    or $\displaystyle z=-\frac{1}{\sqrt2}+\frac{i}{\sqrt2}$
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