Question

write the complex number -√3-i in polar form


NOTE:→ It's an question of class 11 science so please give me the answer according to the grade. If you give me the correct answer than I will mark it as a brainliest answer and if you give me the wrong or unnecessary answer than I will report your answer. Thank you for your cooperation ​​

Answer 1

Answer:

Given,

z = - √3 - i

so,

$|z| = r = \sqrt{ {( - \sqrt{3} )}^{2} + {( - 1)}^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{3 + 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{4} = 2 \\ \\ arg \: z = \theta \: = - \pi + {tan}^{ - 1} ( \frac{ 1}{ \sqrt{3} } ) = - \pi + \frac{\pi}{6} \\ = - \frac{5\pi}{6} \:\:\:\:\:[ \:3rd \: quadrant \:] \\ now \: polar \: form \: \\ r(cos \theta \: + i \: sin \theta) \\ = 2 \{cos \: ( - \frac{5\pi}{6} ) + i \: sin \: ( - \frac{5\pi}{6} ) \} \\ = 2(cos \: \frac{5\pi}{6} - i \: sin \: \frac{5\pi}{6} ) \: \: \: \: \: \: \{ \: cause \: \: \: cos( - \theta) = cos \theta \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: sin( - \theta) = - sin \theta \: \} \\ = answer \\ \\ other \: polar \: form \\ r {e}^{i \theta} \\ = 2 {e}^{i \:( - \frac{ 5\pi}{6} )} \\ = 2 {e}^{ - \frac{i5\pi}{6} }$