If $z_{1},z_{2},z_{3},z_{4}\in \mathbb{C}$ satisfy $z_{1}+z_{2}+z_{3}+z_{4}=0$ and $\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+\left | z_{3} \right |^{2}+\left | z_{4} \right |^{2}=1$, then the least value of $\left | z_{1} -z_{2}\right |^{2}+\left | z_{1} -z_{4}\right |^{2}+\left | z_{2}-z_{3} \right |^{2}+\left | z_{3} -z_{4}\right |^{2}$ is $2$.

asked
Aug 30
in TIFR
soujanyareddy13
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