# How do you multiply  (1-i)(-4-3i)  in trigonometric form?

Jul 8, 2018

color(indigo)((1 - i)* (-4 - 3 i) ~~ -0.28 + i 0.04

#### Explanation:

To divide $\left(1 - i\right) \cdot \left(- 4 - 3 i\right)$ using trigonometric form.

${z}_{1} = \left(1 - i\right) , {z}_{2} = \left(- 4 - 3 i\right)$

r_1 = sqrt(-1^2 + 1^2) = sqrt 2

${r}_{2} = \sqrt{- {3}^{2} + - {4}^{2}} = 5$

${\theta}_{1} = \arctan \left(- \frac{1}{1}\right) = {315}^{\circ} , \text{ IV quadrant}$

${\Theta}_{2} = \arctan \left(- \frac{3}{-} 4\right) = {216.87}^{\circ} , \text{ III quadrant}$

${z}_{1} \cdot {z}_{2} = \left({r}_{1} \cdot {r}_{2}\right) \cdot \left(\cos \left({\theta}_{1} + {\theta}_{2}\right) + i \sin \left({\theta}_{1} + {\theta}_{2}\right)\right)$

${z}_{1} / {z}_{2} = \frac{\sqrt{2}}{5} \cdot \left(\cos \left(315 + 216.87\right) + i \sin \left(315 + 216.87\right)\right)$

${z}_{1} / {z}_{2} = \frac{\sqrt{2}}{5} \cdot \left(\cos \left(531.87\right) + i \sin \left(531.87\right)\right)$

color(indigo)((1 - i)* (-4 - 3 i) ~~ -0.28 + i 0.04#