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

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Answer 1 · 2018-07-08T01:30:36

$\frac{- 2 + 3 i}{4 + i} \approx - 0.2931 - i 0.8231$ $color(maroon)((-2 + 3 i) / (4 + i) ~~ -0.2931 - i 0.8231$

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

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

#r_1 = sqrt(-2^2 + 3^2) = sqrt 13

$r_{2} = \sqrt{4^{2} + 1^{2}} = \sqrt{17}$ $r_2 = sqrt(4^2 + 1^2) = sqrt 17$

$θ_{1} = arctan (- \frac{2}{3}) = {146.31}^{\circ}, II quadrant$ $theta_1 = arctan (-2/3) = 146.31^@, " II quadrant"$

$Theta_2 = arctan(4/1) = 75.96^@, " I quadrant"$

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

$z_1 / z_2 = sqrt(13/17) * (cos (146.31 - 75.96 ) + i sin (146.31 - 75.96 ))$

$z_1 / z_2 = sqrt(13/17) * (cos (70.41) + i sin (70.41))$

$color(maroon)((-2 + 3 i) / (4 + i) ~~ -0.2931 - i 0.8231$

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