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Let z and w are two non zero complex num...

Let `z and w` are two non zero complex number such that `|z|=|w|, and Arg(z)+Arg(w)=pi` then (a) `z=w` (b) `z=overlinew` (c) `overlinez=overlinew` (d) `overlinez=-overlinew`

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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