How do you divide $\frac{7 i + 5}{- 3 i + 8}$ $( 7i+5) / ( -3i +8 )$ in trigonometric form?

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Answer 1 · 2018-06-25T11:23:49

$\frac{5 + 7 i}{8 - 3 i} \approx 0.2603 - i 0.9728$ $color(blue)((5 + 7i) / (8 - 3i) ~~ 0.2603 - i 0.9728$

To divide $\frac{5 + 7 i}{8 - 3 i}$ $(5 +7 i) / (8 - 3i)$ using trigonometric form.

$z_{1} = (5 + 7 i), z_{2} = (8 - 3 i)$ $z_1 = (5 +7 i), z_2 = (8 - 3i)$

#r_1 = sqrt(5^2 + 7^2) = sqrt 74

$r_{2} = \sqrt{8^{2} + - 3^{2}} = \sqrt{73}$ $r_2 = sqrt(8^2 + -3^2) = sqrt 73$

$θ_{1} = arctan (\frac{7}{5}) = {54.46}^{\circ}, I quadrant$ $theta_1 = arctan (7/5) = 54.46^@, " I quadrant"$

$Theta_2 = arctan(-3/8) = 339.44^@, " IV quadrant"$

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

$z_1 / z_2 = sqrt(74/73) * (cos (54.46 - 339.44 ) + i sin (54.46 - 339.44 ))$

$z_1 / z_2 = 1.007 * (cos (-284.98) + i sin (-284.98)) = 1.007 (0.2585 - i 0.966)$

$color(blue)((5 + 7i) / (8 - 3i) ~~ 0.2603 - i 0.9728$

How do you divide ( 7i+5) / ( -3i +8 )7i+5−3i+8( 7i+5) / ( -3i +8 ) in trigonometric form?