MCQ
If $\arg z<0$, then $\arg (-z)-\arg (z)$ is equal to
- ✓$\pi$
- B$-\pi$
- C$-\frac{\pi}{2}$
- D$\frac{\pi}{2}$
✓
Answer
Correct option: A.
$\pi$
(A)
Since $\arg (z)<0$ i.e., -ve
we choose $\arg (z)=-\theta$, where $\theta$ is $+v e$
$\arg (- z )=\pi-\theta$
$\therefore \quad \arg (- z )-\arg ( z )=\pi-\theta+\theta=\pi$
Since $\arg (z)<0$ i.e., -ve
we choose $\arg (z)=-\theta$, where $\theta$ is $+v e$
$\arg (- z )=\pi-\theta$
$\therefore \quad \arg (- z )-\arg ( z )=\pi-\theta+\theta=\pi$
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