# How do you convert -2 - 7i to polar form?

Jun 24, 2018

color(green)("Polar form " = (r, theta) = (7.28, 254.05^@)

#### Explanation:

$z = - 2 - i 7$

$r = \sqrt{- {2}^{2} + - {7}^{2}} = \sqrt{53} = 7.28$

$\theta = {\tan}^{-} 1 \left(- \frac{7}{-} 2\right) = 3.5 = 74.05$

Point lies in the third quadrant.

$\text{Hence } \theta = 180 + 74.05 = {254.05}^{\circ}$

color(green)("Polar form " = (r, theta) = (7.28, 254.05^@)