# How do you write the complex number in trigonometric form -3-i?

Jan 6, 2018

$\sqrt{10} \cdot C i s \left(\pi + \arctan \left(\frac{1}{3}\right)\right)$

#### Explanation:

Magnitute of z=-3-i; $r = \sqrt{{\left(- 3\right)}^{2} + {\left(- 1\right)}^{2}} = \sqrt{10}$

Argument of z; $A r g \left(z\right) = \arctan \left(\frac{- 1}{- 3}\right) = \arctan \left(\frac{1}{3}\right)$

However, z found in 3rd quadrant. Hence,

$z = \sqrt{10} \cdot C i s \left(\pi + \arctan \left(\frac{1}{3}\right)\right)$