If z = frac{-2}{1 + sqrt{3}i},then the value | vedclass

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(C) Given $z = \frac{-2}{1 + \sqrt{3}i}$.Multiply the numerator and denominator by the conjugate $(1 - \sqrt{3}i)$:$z = \frac{-2(1 - \sqrt{3}i)}{(1 +

Vedclass · Accepted Answer

$2\pi/3$

Vedclass · Answer

(C) Given $z = \frac{-2}{1 + \sqrt{3}i}$.Multiply the numerator and denominator by the conjugate $(1 - \sqrt{3}i)$:$z = \frac{-2(1 - \sqrt{3}i)}{(1 + \sqrt{3}i)(1 - \sqrt{3}i)} = \frac{-2 + 2\sqrt{3}i}{1 + 3} = \frac{-2 + 2\sqrt{3}i}{4}$.$z = -\frac{1}{2} + \frac{\sqrt{3}}{2}i$.Since the real part is negative and the imaginary part is positive,$z$ lies in the second quadrant.$arg(z) = \pi - 	an^{-1}\left|\frac{\sqrt{3}/2}{-1/2}ight| = \pi - 	an^{-1}(\sqrt{3}) = \pi - \frac{\pi}{3} = \frac{2\pi}{3}$.

If $z = \frac{-2}{1 + \sqrt{3}i}$,then the value of $arg(z)$ is

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