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)#