# What is the trigonometric form of  (12-2i) ?

Mar 11, 2016

$2 \sqrt{37} \left[\cos \left(- 0.165\right) + i \sin \left(- 0.165\right)\right]$

#### Explanation:

Using the following formulae :

• r^2 = x^2 + y^2

• theta = tan^-1 (y/x)

here x = 12 and y = - 2

hence ${r}^{2} = {12}^{2} + {\left(- 2\right)}^{2} = 148 \Rightarrow r = \sqrt{148} = 2 \sqrt{37}$

and theta = tan^-1(-2/12) ≈ -0.165" radians "

$\Rightarrow \left(12 - 2 i\right) = 2 \sqrt{37} \left[\cos \left(- 0.165\right) + i \sin \left(- 0.165\right)\right]$