How do you divide $\frac{- 4 + 2 i}{3 - i}$ $(-4+2i)/(3-i)$ in trigonometric form?

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Answer 1 · 2018-07-02T11:11:37

$\frac{- 4 + 2 i}{3 - i} \approx - 1.4 - 0.2 i$ $color(maroon)((-4 + 2i) / (3 - i) ~~ -1.4 - 0.2 i$

To divide $\frac{- 4 + 2 i}{3 - i}$ $(-4 + 2 i) / (3 - i)$ using trigonometric form.

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

#r_1 = sqrt(-4^2 + 2^2) = sqrt 20

$r_{2} = \sqrt{3^{2} + - 1^{2}} = \sqrt{10}$ $r_2 = sqrt(3^2 + -1^2) = sqrt 10$

$θ_{1} = arctan (\frac{2}{- 4}) = {153.43}^{\circ}, II quadrant$ $theta_1 = arctan (2/-4) = 153.43^@, " II quadrant"$

$Theta_2 = arctan(-1/3) = 341.57^@, " IV quadrant"$

$z_1 / z_2 = (r_1 / r_2) * (cos (theta_1 - theta_2) + i sin (theta_1 - theta_2))$

$z_1 / z_2 = sqrt(10/20) * (cos (153.43 - 341.57 ) + i sin (153.43 - 341.57 )$

$z_1 / z_2 = sqrt(20/10) * (cos (-188.14) + i sin (-188.14))$

$color(maroon)((-4 + 2i) / (3 - i) ~~ -1.4 - 0.2 i$

How do you divide (-4+2i)/(3-i) −4+2i3−i (-4+2i)/(3-i) in trigonometric form?