# How do you convert 3 + 3i to polar form?

##### 1 Answer
Apr 26, 2016

$\left(3 \sqrt{2} , \frac{\pi}{4}\right)$

#### Explanation:

Using the formulae that links Cartesian to Polar coordinates.

• r^2 = x^2+y^2 rArr r=sqrt(x^2+y^2)

• theta = tan^-1(y/x)

here x = 3 and y = 3

$\Rightarrow r = \sqrt{{3}^{2} + {3}^{2}} = \sqrt{18} = 3 \sqrt{2}$

and $\theta = {\tan}^{-} 1 \left(\frac{3}{3}\right) = {\tan}^{-} 1 \left(1\right) = \frac{\pi}{4}$

$\Rightarrow 3 + 3 i = \left(3 \sqrt{2} , \frac{\pi}{4}\right) \text{ in polar form }$