1. Tardigrade
  2. Question
  3. Mathematics
  4. If arg (z) < 0 , then arg (-z) - arg (z) equals

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $arg (z) < 0$ , then $arg (-z) - arg (z)$ equals

AIEEEAIEEE 2000Complex Numbers and Quadratic Equations

Solution:

Since, $\arg (z) < 0$
$\Rightarrow \arg (z)=-\theta$
image
$\Rightarrow z=r \cos (-\theta)+i \sin (-\theta)$
$=r(\cos \theta-i \sin \theta)$
and $-z=-r[\cos \theta-i \sin \theta]$
$=r[\cos (\pi-\theta)+i \sin (\pi-\theta)]$
$\therefore \arg (-z)=\pi-\theta$
Thus, $\arg (-z)-\arg (z)$
$=\pi-\theta-(-\theta)=\pi$