# How do you write the complex number in trigonometric form sqrt3+i?

Sep 25, 2016

For a number of form, $a + b i$, the form $A \left(\cos \left(\theta\right) + i \sin \left(\theta\right)\right)$ is obtained by using A = sqrt(a² + b² and $\theta = {\tan}^{-} 1 \left(\frac{b}{a}\right)$ (adjust $\theta$ for the proper quadrant)

#### Explanation:

A = sqrt(sqrt3^2 + 1^2

$A = 2$

$\theta = {\tan}^{-} 1 \left(\frac{1}{\sqrt{3}}\right)$

$\theta = \frac{\pi}{6}$

Because the signs of "a" and "b" are positive, we do not adjust the quadrant.

$\sqrt{3} + i = 2 \left(\cos \left(\frac{\pi}{6}\right) + i \sin \left(\frac{\pi}{6}\right)\right)$