Let $z$ be a complex number such that the principal value of argument, arg $z>0$ Then, arg $z-\arg (-z)$ is

• A

  $\frac{\pi}{2}$
• B

  $\pm \pi$
• Correct answer
  C

  $\pi$
• D

  $-\pi$

Solution

$\begin{aligned} \therefore \arg (z)-\arg (-z) &=\theta-(-\pi+\theta) \\ &=\pi \end{aligned}$

Hence, the correct answer is option: 'C'.