Suppose two complex numbers `z=a+ib`, `w=c+id` satisfy the equation `(z+w)/(z)=(w)/(z+w)`. Then

Options

A. both `a` and `c` are zeros
B. both `b` and `d` are zeros
C. both `b` and `d` must be non zeros
D. at least one of `b` and `d` is non zero

Answer

D

Explanation

`(d)` `(z+w)^(2)=zw`
`impliesz^(2)+zw+w^(2)=0`
Let `(z)/(w)=timplies(z)/(w)=(-1+-sqrt(3)i)/(2)`
`argz-argw=(2pi)/(3)` or `argz-argw=-(2pi)/(3)`