# What is the trigonometric form of 5+6i?

Feb 28, 2016

$\sqrt{61} \left[\cos \left(0.876\right) + i \sin \left(0.876\right)\right]$

#### Explanation:

using the following formulae.

• r^2 = x^2 + y^2

• theta = tan^-1 (y/x)

here x = 5 and y = 6

${r}^{2} = {5}^{2} + {6}^{2} = 25 + 36 = 61 \Rightarrow r = \sqrt{61}$

theta = tan^-1(6/5) ≈ 0.876 " radians "

hence the trig. form of 5 + 6i is:

$\sqrt{61} \left[\cos \left(0.876\right) + i \sin \left(0.876\right)\right]$