How do you divide $(4i-5) / (7i+3)$ in trigonometric form?

Question

1349 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-24T05:55:40

$color(brown)(=> 0.8408 ( 0.3 - i 0.9539)$

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

$z_1 = -5 + i 4, z_2 = 3 + i 7$

$r_1 = sqrt(5^2 + 4^2) = sqrt 41$

$theta_1 = tan ^ (-1) (4/-5) = tan ^-1 (-0.8) = -38.66 ^@ = 141.34, " II Quadrant"$

$r_2 = sqrt(3^2 + (7)^2) = sqrt 58$

$theta_2 = tan ^-1 (7/ 3) = 68.8^@$

$z_1 / z_2 = sqrt(41/58) (cos (141.34- 68.8) - i sin (141.34 - 68.8))$

$color(brown)(=> 0.8408 ( 0.3 - i 0.9539)$

How do you divide (4i-5) / (7i+3)(4i-5) / (7i+3) in trigonometric form?