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Thread: Gauss plane set

  1. #1
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    Exclamation Gauss plane set

    a)The set M= {$\displaystyle z \in C : {z^4}$ + 8 - 8 $\displaystyle \sqrt{3}$i =0 }
    Charackterize the set М and point it's the Gauss plane

    b)Where exactly is the Gauss plane image from the number z $\displaystyle \in$ for wich is valid:
    $\displaystyle \left|\frac{z-1}{z-i}\right|$= 1



    Thanks,
    Kukov
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Gauss plane set

    Quote Originally Posted by kukov View Post
    M= {$\displaystyle z \in C : {z^4}$ + 8 - 8 $\displaystyle \sqrt{3}$i =0 } . Charackterize the set М and point it's the Gauss plane
    Find $\displaystyle \sqrt[4]{-8+8\sqrt{8}}=\ldots=\{z_0,z_1,z_2,z_3\}$

    Where exactly is the Gauss plane image from the number z $\displaystyle \in$ for wich is valid: $\displaystyle \left|\frac{z-1}{z-i}\right|$= 1
    Equivalently, $\displaystyle |z-1|=|z-i|$ or $\displaystyle d(z,1)=d(z,i)$ and we get the perpendicular bisector of a determined line segment.
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