2010/019) Suppose two complex numbers z = a + ib and w = c + id

Suppose two complex numbers z = a + ib and w = c + id satisfy the equation ...?
(z + w)/z = w/(z + w).

Then,
a) both a and c are zero;
b) both b and d are zero;
c) both b and d must be non zero;
d) at least one of b and d is non-zero;
Kindly explain...

(z + w)/z = w/(z + w)
=> (z+w)^2 = wz
=> z^2+wz+w^2 = 0

let z/w = t so we get

t^2+t+1 = 0 and hence t is cube root of 1 that is cis 120 or cis 240

so z and w in complex plane and at angle 120

so at least one of b and d must be non zero because in case b and d both are zero then z/w is real

hence ans is d