• # question_answer Let $z,w$be complex numbers such that $\overline{z}+i\overline{w}=0$and $arg\,\,zw=\pi$. Then arg z equals [AIEEE 2004] A) $5\pi /4$ B) $\pi /2$ C) $3\pi /4$ D) $\pi /4$

Given that arg  zw =$\pi$            .....(i) $\bar{z}+i\bar{\omega }=0\Rightarrow \bar{z}=-i\bar{\omega }$$\Rightarrow z=i\omega$$\Rightarrow \omega =-iz$ From (i), arg$(-i{{z}^{2}})=\pi$ $arg\ (-i)+2arg(z)=\pi$ ; $\frac{-\pi }{2}+2\ arg(z)=\pi$ $2\,arg\,(z)=\frac{3\pi }{2}$; $a\,rg(z)=\frac{3\pi }{4}$