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Math Help - 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 \overline{z} in the first equation:

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

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

    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 z=a+ib

    a) \overline{z}z=1

    (a-ib)(a+ib)=1

    a^2+b^2=1 ---------- (1)

    b) iz=\overline{z}

    i(a+ib)=(a-ib)

    ai-b=a-ib

    Equating real and imaginary parts, we get

    a=-b

    Substituting this in (1), we get

    2a^2=1

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

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

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

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