Question

Write z= root 3 - iota in polar form and find z and modulus of z​

Answer 1

Given:

$\large\rm { z = \sqrt{3} - \iota}$

Modulus:

$\large\rm { |z| = \sqrt{ (- \sqrt{3})^{2} +1^{2}}}$

$\large\rm { \ \ \ \ \ = \sqrt{3+1}}$

$\large\rm {\ \ \ \ \ = 2}$

$\large\rm { |z| = 2}$

Argument

$\large\rm { \theta = \tan^{-1} \frac{b}{a}}$

$\large\rm { = \tan^{-1} \frac{1}{ - \sqrt{3} } }$

$\large\rm { \ \ \ \ \ = -30}$

$\large\rm { \therefore \theta = 180-30 = 150}$

$\large\rm { \theta = 150 \times \frac{\pi}{180}}$

$\large\rm { \theta = \frac{5 \pi}{6}}$