Convert the given complex number in polar for | vedclass

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

Question

(A) Let the complex number be $z = \sqrt{3} + i$.The polar form is given by $z = r(\cos 	heta + i \sin 	heta)$,where $r = |z| = \sqrt{(\sqrt{3})^2 +

Vedclass · Accepted Answer

$2(\cos \frac{\pi}{6} + i \sin \frac{\pi}{6})$

Vedclass · Answer

(A) Let the complex number be $z = \sqrt{3} + i$.The polar form is given by $z = r(\cos 	heta + i \sin 	heta)$,where $r = |z| = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3+1} = \sqrt{4} = 2$.We have $r \cos 	heta = \sqrt{3}$ and $r \sin 	heta = 1$.Substituting $r = 2$,we get $\cos 	heta = \frac{\sqrt{3}}{2}$ and $\sin 	heta = \frac{1}{2}$.Since both $\cos 	heta$ and $\sin 	heta$ are positive,$	heta$ lies in the $I$ quadrant.The principal argument $	heta = \frac{\pi}{6}$.Thus,the polar form is $2(\cos \frac{\pi}{6} + i \sin \frac{\pi}{6})$.

Convert the given complex number in polar form: $\sqrt{3}+i$

Similar Questions

The amplitude of $\sin \frac{\pi}{5} + i(1 - \cos \frac{\pi}{5})$ is:

The amplitude of the complex number $z = \sin \alpha + i(1 - \cos \alpha )$ is

Let $z$ satisfy $|z| = 1$ and $z = 1 - \bar{z}$.
Statement $1$: $z$ is a real number.
Statement $2$: The principal argument of $z$ is $\frac{\pi}{3}$.

The sum of the argument of $z$ and another complex number is $\pi$. The other complex number can be written as:

If $z_1=(2,-1)$ and $z_2=(6,3)$,then $\operatorname{amp}\left(\frac{z_1-z_2}{z_1+z_2}\right)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module