Question

z=√3-i, find its polar form


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Answer 1

EXPLANATION :

$\bigstar \: \: \: \: \bf{Given :}$

$\sf \: z = \sqrt{3} + i$

$\bigstar \: \: \: \: \: \bf{Solution :}$

$\sf \: Argument , \\ \: \tan \theta = \frac{1}{ \sqrt{3} } \\ \implies \sf \underline{\theta \: = \frac{\pi}{6} }$

$\sf \: Modulus, \\ \sf |z| = \sqrt{ {1}^{2} + { \sqrt{3} }^{2} } \\ \implies \: \sf{\underline{|z| = 2}}$

$\sf \therefore \:The \: polar \: form \: is \\ \sf \: \boxed{ \boxed{ \mathfrak{z = 2( \sin \: \frac{\pi}{6} + \cos \frac{ \pi}{6} )}}}$

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HOPE THIS IS HELPFUL...