Mathematics - Complex Number Question with Solution | TestHub

As $z_1+z_2+z_3=0\Rightarrow z_1,z_2,z_3$ are vertices of an equilateral triangle and $z_4,z_5$ are end points of diameter. So, ${\left|z_i-z_j\right|}^2=3r^2$ if $i,j\in \{1,2,3\};{\left|z_i-z_j\right|}^2=4r^2$ if $i\in \{1,2,3\}\&j\in \{4,5\}\&{\left|z_4-z_5\right|}^2=4r^2$

$\Rightarrow {\sum }_{1\le i<j<5}\sum {\left|z_i-z_j\right|}^2=25r^2=3600$.