How do you divide $\frac{- 1 + 4 i}{3 - 7 i}$ $(-1+4i)/(3-7i)$ in trigonometric form?

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How do you divide $\frac{- 1 + 4 i}{3 - 7 i}$ $(-1+4i)/(3-7i)$ in trigonometric form?

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Answer 1 · 2018-07-30T03:17:20

$\Rightarrow - 0.5345 + 0.0862 i, II Quadrant$ $color(violet)(=> -0.5345 + 0.0862 i, " II Quadrant"$

Explanation:

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

$z_{1} = - 1 + 4 i, z_{2} = 3 - 7 i$ $z_1 = -1 + 4i, z_2 = 3 - 7 i$

$r_{1} = {\sqrt{- 1^{2} + 4^{2}}}^{2}) = \sqrt{17}$ $r_1 = sqrt(-1^2 + 4^2)^2) = sqrt 17$

$θ_{1} = {tan}^{- 1} (\frac{4}{- 1}) {104.0362}^{\circ}, II Quadrant$ $theta_1 = tan ^-1 (4/ -1) 104.0362^@ , " II Quadrant"$

$r_{2} = \sqrt{3^{2} + {(- 7)}^{2}} = \sqrt{58}$ $r_2 = sqrt(3^2 + (-7)^2) = sqrt 58$

$θ_{2} = {tan}^{- 1} (- \frac{7}{3}) \approx {293.1986}^{\circ}, IV Quadrant$ $theta_2 = tan ^-1 (-7/ 3) ~~ 293.1986^@, " IV Quadrant"$

$\frac{z_{1}}{z_{2}} = \sqrt{\frac{17}{58}} (cos (104.0362 - 293.1986) + i sin (104.0362 - 293.1986))$ $z_1 / z_2 = sqrt(17 / 58) (cos (104.0362 - 293.1986) + i sin (104.0362 - 293.1986))$

$\Rightarrow - 0.5345 + 0.0862 i, II Quadrant$ $color(violet)(=> -0.5345 + 0.0862 i, " II Quadrant"$

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How do you divide $\frac{- 1 + 4 i}{3 - 7 i}$ $(-1+4i)/(3-7i)$ in trigonometric form?

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How do you divide $\frac{- 1 + 4 i}{3 - 7 i}$ $(-1+4i)/(3-7i)$ in trigonometric form?