AIEEE 2004 (Offline)Question 1
Let $z$ and $w$ be complex numbers such that $\bar z+i\bar w=0$ and $\arg zw=\pi$. Then $\arg z$ equals :
Complex Numbers
Solution
$\bar z=-i\bar w\Rightarrow z=iw$, so $zw=iw^2$, $\arg(zw)=\frac\pi2+2\arg w=\pi$, $\arg w=\frac\pi4$ (or $-\frac{3\pi}4$). Then $\arg z=\arg w+\frac\pi2=\frac{3\pi}4$.