# How do you divide ( -4i+2) / (i+7) in trigonometric form?

In trigonometric form : $0.632 \left[\cos \left(- 71.565\right) + i \sin \left(- 71.565\right)\right]$
$\frac{- 4 i + 2}{i + 7} = \frac{\left(- 4 i + 2\right) \left(i - 7\right)}{\left(i + 7\right) \left(i - 7\right)} = \frac{- 4 \cdot {i}^{2} - 14 + 30 \cdot i}{{i}^{2} - {7}^{2}} = \left(- \frac{1}{50}\right) \cdot \left(- 10 + 30 i\right) = 0.2 - 0.6 i$. Let $Z = 0.2 - 0.6 i$ Modulas Z= $\sqrt{{0.2}^{2} + {\left(- 0.6\right)}^{2}} = .632$ Argument Z $\theta = {\tan}^{-} 1 \left(\frac{- 0.6}{0.2}\right) = {\tan}^{-} 1 \left(- 3\right) = - {71.565}^{0}$ Hence Z expressed in trigonometric form: $0.632 \left[\cos \left(- 71.565\right) + i \sin \left(- 71.565\right)\right]$[Ans]