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Let $z, w$ be complex numbers such that $\bar{z}+i \bar{w}=0$ and $\arg z w=\pi .$ Then arg $z$ equals

1) $\frac{\pi}{4}$
2) $\frac{5 \pi}{4}$
3) $\frac{3 \pi}{4}$
4) $\frac{\pi}{2}$
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(3) Here $\omega=\frac{z}{i} \Rightarrow \arg \left(Z, \dfrac{Z}{i}\right)=\pi$

$\Rightarrow 2 \arg (z)-\arg (\mathrm{i})=\pi \quad \Rightarrow \arg (z)=\dfrac{3 \pi}{4} .$
by Diamond (75,914 points)

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