How do you divide $\frac{3 i - 1}{- 8 i + 3}$ $( 3i-1) / (-8i +3 )$ in trigonometric form?

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Answer 1 · 2018-06-28T04:28:37

$\frac{- 1 + 3 i}{3 - 8 i} \approx - 0.3666 - i 0.0508$ $color(maroon)((-1 + 3i) / (3 - 8i) ~~ -0.3666 - i 0.0508$

To divide $\frac{- 1 + 3 i}{3 - 8 i}$ $(-1 + 3 i) / (3 - 8i)$ using trigonometric form.

$z_{1} = (- 1 + 3 i), z_{2} = (3 - 8 i)$ $z_1 = (-1 + 3 i), z_2 = (3 - 8i)$

#r_1 = sqrt(3^2 + 1^2) = sqrt 10

$r_{2} = \sqrt{87^{2} + - 3^{2}} = \sqrt{73}$ $r_2 = sqrt(87^2 + -3^2) = sqrt 73$

$θ_{1} = arctan (- \frac{3}{1}) = {108.43}^{\circ}, II quadrant$ $theta_1 = arctan (-3/1) = 108.43^@, " II quadrant"$

$Theta_2 = arctan(-8/3) = 290.56^@, " IV quadrant"$

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

$z_1 / z_2 = sqrt(10/53) * (cos (108.43 - 290.56 ) + i sin (108.43 - 290.56 ))$

$z_1 / z_2 = sqrt910/53) * (cos (-172.13) + i sin (-172.13))$

$color(maroon)((-1 + 3i) / (3 - 8i) ~~ -0.3666 - i 0.0508$

How do you divide ( 3i-1) / (-8i +3 )3i−1−8i+3( 3i-1) / (-8i +3 ) in trigonometric form?