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Suppose two complex numbers z=a+ib, w=c+...

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

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

Text Solution

Verified by Experts

The correct Answer is:
D
`(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)`
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