If $z=1+i \sqrt{3}$ then $|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|$ is equal to

  • A
    $0$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{2 \pi}{3}$

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