# How do you add (7+9i)+(2+i) in trigonometric form?

Oct 24, 2016

$= \sqrt{181} \cdot \left(\cos \left(0.83798\right) + i \sin \left(0.83798\right)\right)$

#### Explanation:

It is usually easier to simplify cartesian form and then convert to trigonometric afterwards,

$\left(7 + 9 i\right) + \left(2 + i\right)$

$9 + 10 i$

now we convert to trigonometric.

$9 + 10 i = r \cdot c i s \left(\theta\right)$

$r = \sqrt{{9}^{2} + {10}^{2}}$

$r = \sqrt{181}$

$\theta = {\tan}^{-} 1 \left(\frac{10}{9}\right)$

$\theta = 0.83798$

giving us,

$\left(7 + 9 i\right) + \left(2 + i\right) = \sqrt{181} \cdot c i s \left(0.83798\right)$

or in expanded form,

$= \sqrt{181} \cdot \left(\cos \left(0.83798\right) + i \sin \left(0.83798\right)\right)$