# How do you write the complex number in trigonometric form 2+2i?

Jun 15, 2017

$2 \sqrt{2} \left(\cos \left(\frac{\pi}{4}\right) + i \sin \left(\frac{\pi}{4}\right)\right)$

#### Explanation:

$\text{to convert from "color(blue)"standard to trigonometric form}$

$\text{that is " x+yitor(costheta+isintheta)" where }$

• r=sqrt(x^2+y^2)

• theta=tan^-1(y/x)

$\text{here " x=2" and } y = 2$

$\Rightarrow r = \sqrt{{2}^{2} + {2}^{2}} = \sqrt{8} = 2 \sqrt{2}$

$\theta = {\tan}^{-} 1 \left(\frac{2}{2}\right) = {\tan}^{-} 1 \left(1\right) = \frac{\pi}{4}$

$\Rightarrow 2 + 2 i = 2 \sqrt{2} \left(\cos \left(\frac{\pi}{4}\right) + i \sin \left(\frac{\pi}{4}\right)\right)$