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Assertion (A) If the arguments of $\bar{z}_1$ and $z_2$ are $\frac{\pi}{5}$ and $\frac{\pi}{3}$ respectively, then $\arg \left(z_1 z_2\right)$ is $\frac{2 \pi}{15}$. Reason (R) For any complex number $z$, $\arg \bar{z}=\frac{\pi}{2}+\arg z$
The correct option among the following is
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The correct option among the following is
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The correct answer is:
$(A)$ is true but $(R)$ is false
We have, $\arg \left(\bar{z}_1\right)=\frac{\pi}{5}, \arg \left(z_2\right)=\frac{\pi}{3}$
$\therefore \quad \arg \left(z_1 z_2\right)=\arg \left(z_2\right)-\arg \left(\bar{z}_1\right)=\frac{\pi}{3}-\frac{\pi}{5}=\frac{2 \pi}{15}$
Also, $\arg (\bar{z})=-\arg (z)$.
(A) is ture but (R) is false.
$\therefore \quad \arg \left(z_1 z_2\right)=\arg \left(z_2\right)-\arg \left(\bar{z}_1\right)=\frac{\pi}{3}-\frac{\pi}{5}=\frac{2 \pi}{15}$
Also, $\arg (\bar{z})=-\arg (z)$.
(A) is ture but (R) is false.
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