Convert the given complex number in polar for | vedclass

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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: $\sqrt{3}+i$

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