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

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

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Answer 1 · 2018-07-08T03:51:54

$\Rightarrow 026 - 0.18 i$ $color(green)(=> 026 - 0.18 i)$

Explanation:

$\frac{z_{1}}{z_{2}} = (\frac{r_{1}}{r_{2}}) (cos (θ_{1} - θ_{2}) + i sin (θ_{1} - θ_{2}))$ $z_1 / z_2 = (r_1 / r_2) (cos (theta_1 - theta_2) + i sin (theta_1 - theta_2))$

$z_{1} = 2 - i 3, z_{2} = 7 - i$ $z_1 = 2 - i 3, z_2 = 7 - i$

$r_{1} = \sqrt{2^{2} + - 1^{2}} = \sqrt{5}$ $r_1 = sqrt(2^2 + -1^2) = sqrt 5$

$θ_{1} = {tan}^{- 1} (- \frac{1}{2}) = {333.43}^{\circ}, IV Quadrant$ $theta_1 = tan ^ (-1) (-1/2) = 333.43 ^@, " IV Quadrant"$

$r_{2} = \sqrt{7^{2} + {(- 1)}^{2}} = \sqrt{50}$ $r_2 = sqrt(7^2 + (-1)^2) = sqrt 50$

$θ_{2} = {tan}^{- 1} (- \frac{1}{7}) = {303.69}^{\circ}, IV Quadrant$ $theta_2 = tan ^-1 (-1/ 7) = 303.69^@, " IV Quadrant"$

$\frac{z_{1}}{z_{2}} = \sqrt{\frac{5}{50}} (cos (333.43 - 351.87) + i sin (333.43 - 351.87))$ $z_1 / z_2 = sqrt(5/50) (cos (333.43- 351.87) + i sin (333.43- 351.87))$

$\Rightarrow 026 - 0.18 i$ $color(green)(=> 026 - 0.18 i)$

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

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