Question

If $\arg \left(z\right)<0$, then $\arg (-z)-\arg \left(z\right)=$

• A. $\pi$
• B. $-\pi$
• C. $-\frac{\pi }{2}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (A)

$\pi$

Ans. $\left(a\right).$ Since arg $z<0$ i.e. $-ive$, we choose arf $z=-\theta$, where $\theta$ is $+ive$
$\therefore \arg (-z)=-[\pi -(-\theta )=-\pi -\theta =2\pi +(-\pi -\theta )]$
$=\pi +(-\theta )=\pi +$ arg $z$
$\therefore \arg (-z)-$ arg $z=\pi$