# How do you add (2-8i)+(-2+4i) in trigonometric form?

Dec 23, 2015

$\left(2 - 8 i\right) + \left(- 2 + 4 i\right) = 4 \left(\cos \left(\frac{3 \pi}{2}\right) + i \sin \left(\frac{3 \pi}{2}\right)\right)$

#### Explanation:

I will assume that we are allowed to do the addition in rectangular form and then convert the answer into trigonometric form.

{: (,,"(",2,-8i,")"), ("+",,"(",-2,+4i,")"), (,,,"-------","-------",), ("=",,"(",0,-4i,")") :}

The general trigonometric form is
$\textcolor{w h i t e}{\text{XXX}} \left\mid z \right\mid \left(\cos \left(\theta\right) + i \sin \left(\theta\right)\right)$
where
$\textcolor{w h i t e}{\text{XXX}} \left\mid z \right\mid$ is the distance from the origin (in the complex plane)
and
$\textcolor{w h i t e}{\text{XXX}}$theta# is the angle of the point (relative to the positive Real axis in the complex plane)