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

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Answer 1 · 2018-06-15T04:10:59

$color(crimson)(=> 0.42 ( -0.7475 + i 0.6643)$

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

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

$r_1 = sqrt(1 + 3^2) = sqrt10$

$theta_1 = tan ^ (-1) (1/-3) = -18.43 = 161.57^@, " II Quadrant"$

$r_2 = sqrt(7^2 + 3^2) = sqrt58$

$theta_2 = tan ^ (-1) (3/7) = 23.2^@$

$z_1 / z_2 = sqrt(10/58) (cos (161.57- 23.2) - i sin (161.57 - 23.2))$

$color(crimson)(=> 0.42 ( -0.7475 + i 0.6643)$

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