# What is the trigonometric form of  (-5+11i) ?

Jan 9, 2016

$\sqrt{146} \left(\cos \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right)\right)$

#### Explanation:

Trigonometric form of a complex number $x + i y$ is given by

r(cos(theta)+isin(theta)
Where,
$r = \sqrt{{x}^{2} + {y}^{2}}$
$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$

Our complex number is $- 5 + 11 i$

$r = \sqrt{{\left(- 5\right)}^{2} + {11}^{2}}$
$r = \sqrt{25 + 121}$
$r = \sqrt{146}$

$\theta = {\tan}^{-} 1 \left(- \frac{11}{5}\right)$

The complex number in trigonometric form is

$\sqrt{146} \left(\cos \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{11}{5}\right)\right)\right)$