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

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

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Let $z=r(cos\theta+isin\theta)$
$arg(z)=\theta<0$
$-z=-r(cos\theta+isin\theta)$
$=r(cos(\pi+\theta)+isin(\pi+\theta))$
$arg(-z)=\pi+\theta$
$\therefore\:arg(-z)-arg(z)=\pi+\theta-\theta=\pi$
answered Jul 15, 2013 by rvidyagovindarajan_1
 

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