Let z and w be complex numbers such that z+iw=0 and (zw)=.

Question

Let $z$ and $w$ be complex numbers such that $z+iw=0$ and $\arg(zw)=\pi$. Then $\arg z$ equals

Accepted Answer

$z=-iw \implies \arg z=\dfrac\pi2+\arg w$ (adjusting branch). Also $\arg z+\arg w=\pi$. Solving: $\arg z=\dfrac{3\pi}4.$

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