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The argument of $\large\frac{1-\sqrt 3i}{1+\sqrt 3i}=?$

(A) $\large\frac{\pi}{3}$

(B) $\large\frac{2\pi}{3}$

(C) $\large\frac{4\pi}{3}$

(D) $\large-\frac{\pi}{3}$

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1 Answer

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  • $Arg\big(\large\frac{z_1}{z_2}\big)=$$Arg(z_1)-Arg(z_2)$
$Arg(1-\sqrt 3i)=2\pi-\large\frac{\pi}{3}=\frac{5\pi}{3}$
$Arg(1+\sqrt 3i)=\large\frac{\pi}{3}$
$Arg\bigg(\large\frac{1-\sqrt 3i}{1+\sqrt 3i}\bigg)=$$Arg(1-\sqrt 3i)-Arg(1+\sqrt 3i)$
$=\large\frac{5\pi}{3}-\frac{\pi}{3}=\frac{4\pi}{3}$
answered Jul 28, 2013 by rvidyagovindarajan_1
 

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