# How do you write 6+0i in trigonometric form?

Feb 11, 2016

$6 \left(\cos 0 + i \cdot \sin 0\right)$

#### Explanation:

Trigonometric form of $a + b i$ is $r \left(\cos \theta + \sin \theta\right)$

As such $r$ is $\sqrt{{a}^{2} + {b}^{2}}$ and $\theta = {\tan}^{- 1} \left(\frac{b}{a}\right)$

Here $a = 6$ and $b = 0$, hence

$r = \sqrt{{6}^{2} + {0}^{2}} = 6$ and $\theta = {\tan}^{- 1} 0 = 0$

Hence $6 + 0 i$ in trigonometric form is $6 \left(\cos 0 + i \cdot \sin 0\right)$.