Question

If| z1| = |z2| = ... = |zn | = 1 , then

show that |z1+z2+z3+.....zn| = |1/z1 + 1/z2 + 1/z3 + ...+1/zn|

Answer 1

Given that, | z1| = |z2| = ... = |zn | = 1