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If the $\operatorname{Arg} z_1$ and $\operatorname{Arg} \overline{z_2}$ are $\frac{\pi}{3}$ and $\frac{\pi}{5}$ respectively then the value of $\operatorname{Arg} z_1+\operatorname{Arg} z_2$ is
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The correct answer is:
$\frac{2 \pi}{15}$
Given that $\operatorname{Arg} \mathrm{z}_1=\left|\frac{\neq}{3}\right|$
$\begin{aligned} & \operatorname{Arg} \mathrm{Z}_2=-\operatorname{Arg} \overline{\mathrm{Z}}_2=-\frac{\pi}{5} \\ & \therefore \mathrm{Z}_1+\operatorname{Arg} \mathrm{Z}_2=\frac{\pi}{3}-\frac{\pi}{5}=\frac{2 \pi}{15}\end{aligned}$
$\begin{aligned} & \operatorname{Arg} \mathrm{Z}_2=-\operatorname{Arg} \overline{\mathrm{Z}}_2=-\frac{\pi}{5} \\ & \therefore \mathrm{Z}_1+\operatorname{Arg} \mathrm{Z}_2=\frac{\pi}{3}-\frac{\pi}{5}=\frac{2 \pi}{15}\end{aligned}$
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