How do you divide $\frac{- 4 i + 2}{i + 7}$ $( -4i+2) / (i+7)$ in trigonometric form?

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How do you divide $\frac{- 4 i + 2}{i + 7}$ $( -4i+2) / (i+7)$ in trigonometric form?

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Answer 1 · 2016-05-06T10:58:41

In trigonometric form : $0.632 [cos (- 71.565) + i sin (- 71.565)]$ $0.632[cos(-71.565)+i sin(-71.565)]$

Explanation:

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

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How do you divide $\frac{- 4 i + 2}{i + 7}$ $( -4i+2) / (i+7)$ in trigonometric form?

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How do you divide $\frac{- 4 i + 2}{i + 7}$ $( -4i+2) / (i+7)$ in trigonometric form?