# What is the trigonometric form of  (-1+6i) ?

Dec 28, 2015

$\sqrt{37} \angle - 1 , 4$

#### Explanation:

A complex number $x + i y$ in rectangular form may be converted to polar form $r \angle \theta$ (trigonometric form) as follows :

$r = \sqrt{{x}^{2} + {y}^{2}} \mathmr{and} \theta = {\tan}^{- 1} \left(\frac{y}{x}\right)$.

So in this particular case we get :

$r = \sqrt{{\left(- 1\right)}^{2} + {6}^{2}} = \sqrt{37}$

$\theta = {\tan}^{- 1} \left(\frac{6}{- 1}\right) = - 80 , {5}^{\circ} = - 1 , 4 r a d$