If |z1|=|z2|=|z3|=|z4|=1 and z1+z2+z3+z4=0
then least value of the expression
E=|z1−z2|2+|z2−z3|2+|z3−z4|2+|z4−z1|2 is
8
E=2(|z1|2+|z2|2+|z3|2+|z4|2)
−¯z1(z2+z4)−¯z2(z1+z3)−¯z3(z2+z4)−¯z4(z1+z3)=2(|z1|2+|z2|2+|z3|2+|z4|2)
−(¯z1+¯z3)(z2+z4)−(¯z2+¯z4)(z1+z3)=8+|z1+z3|2+|z2+z4|2≥8
∵z1+z3=−(z2+z4)