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Math Help - Equation in c

  1. #1
    Super Member dhiab's Avatar
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    Equation in c

    Solve in C :

    n is in N and is the conjucate of .
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  2. #2
    MHF Contributor red_dog's Avatar
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    (z-1)^n=(\overline{z}+1)^n\Rightarrow\left(\frac{z-1}{\overline{z}+1}\right)^n=1

    Apply the modulus to both members. Then
    \left|\frac{z-1}{\overline{z}+1}\right|=1\Rightarrow|z-1|=|\overline{z}+1|

    Let z=x+yi

    (x-1)^2+y^2=(x+1)^2+y^2\Rightarrow x=0, \ y\in\mathbb{R}

    So, z=yi

    Replace y in the equation: (-1+yi)^n=(1-yi)^n\Rightarrow(-1+yi)^n=(-1)^n(-1+yi)^n

    If n is even the equation is verified for every real y.

    If n is odd the equation has no solution.
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