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Math Help - Gauss plane set

  1. #1
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    Exclamation Gauss plane set

    a)The set M= { z \in  C :   {z^4} + 8 - 8 \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 \in for wich is valid:
    \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= { z \in  C :   {z^4} + 8 - 8 \sqrt{3}i =0 } . Charackterize the set М and point it's the Gauss plane
    Find \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 \in for wich is valid: \left|\frac{z-1}{z-i}\right|= 1
    Equivalently, |z-1|=|z-i| or d(z,1)=d(z,i) and we get the perpendicular bisector of a determined line segment.
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