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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

If $\sqrt{3} + i = (a + ib)(c + id)$,then $\tan^{-1}\left(\frac{b}{a}\right) + \tan^{-1}\left(\frac{d}{c}\right)$ has the value

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

Let $z_1$ and $z_2$ be two complex numbers with $\alpha$ and $\beta$ as their principal arguments such that $\alpha + \beta > \pi$,then the principal argument of $z_1 z_2$ is given by:

The amplitude of ${e^{{e^{ - i\theta }}}}$ is equal to

The argument of the complex number $\sin \frac{6\pi}{5} + i(1 + \cos \frac{6\pi}{5})$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module