Thread: Minimum value of complex P(z)

1. 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 $i=\sqrt{-1}$

2. 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.