# What is the trigonometric form of  (5+10i)(3+3i) ?

May 3, 2018

$15 \setminus \sqrt{10} \textrm{c i s} \left(\textrm{A r c} \textrm{\tan} \left(- 3\right)\right)$

#### Explanation:

$\left(5 + 10 i\right) \left(3 + 3 i\right) = 15 \left(1 + 2 i\right) \left(1 + i\right) = 15 \left(- 1 + 3 i\right)$

$= 15 \setminus \sqrt{{1}^{2} + {3}^{2}} \left(\textrm{c i s} \left(\arctan 2 \left(3 / , - 1\right)\right)\right\}$

I employ the funny notation because it take a two parameter, four quadrant arctangent in general. This one's in the fourth quadrant, so the principal value of the arctangent is sufficient:

$= 15 \setminus \sqrt{10} \textrm{c i s} \left(\textrm{A r c} \textrm{\tan} \left(- 3\right)\right)$