Browse Questions

# If $arg(z)<0$, then $arg(-z)-arg(z)$ = ?

$\begin{array}{1 1}(A) \;\pi \\(B)\; \large\frac{\pi}{2}\\(C)\;\large\frac{-\pi}{2}\\(D)\;-\pi \end{array}$

Let $z=r(cos\theta+isin\theta)$
$arg(z)=\theta<0$
$-z=-r(cos\theta+isin\theta)$
$=r(cos(\pi+\theta)+isin(\pi+\theta))$
$arg(-z)=\pi+\theta$
$\therefore\:arg(-z)-arg(z)=\pi+\theta-\theta=\pi$