Question

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`

Answer 1

Correct Answer - 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`