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Math Help - Minimum value of complex P(z)

  1. #1
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    Minimum value of complex P(z)

    Let P(z) = \left|2z-1-i\right|+\left|3z-2-2i\right|+\left|4z-3-3i\right| then find Minimum value of P(z) also find corrosponding complex number z.

    Where i=\sqrt{-1}
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Minimum value of complex P(z)

    Hint:

    p(z)=2|z-z_1|+3|z-z_2|+4|z-z_3|=2d(z,z_1)+3d(z,z_2)+4d(z,z_3) where

    z_1=\frac{1}{2}+\frac{1}{2}i,z_2=\frac{2}{3}+\frac  {2}{3}i,z_3=\frac{3}{4}+\frac{3}{4}i are collinear.
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