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z and omega are two nonzero complex numb...

z and `omega` are two nonzero complex number such that `|z|=|omega|" and "Argz+Arg omega= pi` then z equals

A

w

B

`-w`

C

`bar w`

D

`- bar w`

Text Solution

Verified by Experts

The correct Answer is:
D
Since |z|=|w| and arg (z)=`pi`-arg (w)
Let `w=re^(I theta) , then bar w =re^(-ite)`
`therefore z= re^i(pi - theta)= re ^(I pi).e^(-I theta)=-bar w`
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