# How do you add (-1+3i)+(7-3i) in trigonometric form?

Feb 26, 2016

Adding in rectangular form then converting to trigonometric form gives
$\textcolor{w h i t e}{\text{XXX}} 6 \left(\cos \left(0\right) + i \sin \left(0\right)\right)$

#### Explanation:

Confession: I don't know any easy way to do the addition in trigonometric form (multiplication and division is relatively easy).

$\textcolor{w h i t e}{\text{XXX}} \left(- 1 + 3 i\right) + \left(7 - 3 i\right)$
$\textcolor{w h i t e}{\text{XXXXXX}} = \left(- 1 + 7\right) + \left(3 i - 3 i\right)$
$\textcolor{w h i t e}{\text{XXXXXX}} = 6 + 0 i$
which translates easily into trigonometric form $r \left(\cos \left(\theta\right) + i \sin \left(\theta\right)\right)$
with $r = \sqrt{{6}^{2} + {0}^{2}} = 6$
and $\theta = \arctan \left(\frac{0}{6}\right) = \arctan \left(0\right) = 0$