Assertion $(A)$: If the arguments of $\bar{z}_1$ and $z_2$ are $\frac{\pi}{5}$ and $\frac{\pi}{3}$ respectively,then $\arg(z_1 z_2)$ 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:

• A
  $(A)$ is true,$(R)$ is true and $(R)$ is the correct explanation for $(A)$
• B
  $(A)$ is true,$(R)$ is true but $(R)$ is not the correct explanation for $(A)$
• C
  $(A)$ is true but $(R)$ is false
• D
  $(A)$ is false but $(R)$ is true