If z = frac{1 - isqrt{3}}{1 + isqrt{3}},then | vedclass

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

Question

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

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(C) Given $z = \frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}$.Multiply the numerator and denominator by the conjugate of the denominator $(1 - i\sqrt{3})$:$z = \frac{(1 - i\sqrt{3})(1 - i\sqrt{3})}{(1 + i\sqrt{3})(1 - i\sqrt{3})} = \frac{1 - 3 - 2i\sqrt{3}}{1 + 3} = \frac{-2 - 2i\sqrt{3}}{4} = -\frac{1}{2} - i\frac{\sqrt{3}}{2}$.Since the complex number $z = x + iy$ lies in the third quadrant $(x $arg(z) = 180^\circ + 	an^{-1}\left(\frac{-\sqrt{3}/2}{-1/2}ight) = 180^\circ + 	an^{-1}(\sqrt{3}) = 180^\circ + 60^\circ = 240^\circ$.Alternatively,using the property $arg(\frac{z_1}{z_2}) = arg(z_1) - arg(z_2)$:$arg(z) = arg(1 - i\sqrt{3}) - arg(1 + i\sqrt{3}) = -60^\circ - 60^\circ = -120^\circ$.Since $-120^\circ$ is equivalent to $360^\circ - 120^\circ = 240^\circ$,the correct answer is $240^\circ$.

If $z = \frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}$,then $arg(z) = $ ............. $^\circ$

Similar Questions

If ${z_1}, {z_2}$ and ${z_3}, {z_4}$ are two pairs of conjugate complex numbers,then $arg\left( \frac{z_1}{z_4} \right) + arg\left( \frac{z_2}{z_3} \right)$ equals:

Let $z$ be a purely imaginary number such that $\text{Im}(z) < 0$. Then $\arg(z)$ is equal to

If $z$ and $w$ are complex numbers such that $\bar{z} - i \bar{w} = 0$ and $\operatorname{Arg}(zw) = \frac{3 \pi}{4}$,then $\operatorname{Arg} z =$

The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} - i}$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module