Question

a,b,c are complex numbers:
prove: if |a|=|b|=|c|=1 then (conjugate of)(a+b+c)=
1/a+1/b+1/c

Answer 1

If |a|=|b|=|c|=1, then a,b,c all lie on the unit circle an may be written as
a = e^(pi)
b = e^(qi)
c = e^(ri)
for real numbers, p, q, r.

Then a* (conjugate) = e^(-pi) = (e^(pi))^-1 = 1/a,
b* = 1/b and c* = 1/c.

Therefore (a+b+c)* = ...