How do you divide #( 4i+1) / (-8i +3 )# in trigonometric form?

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Answer 1 · 2018-06-28T04:02:35

#color(blue)((1 + 4i) / (3 - 8i) ~~ 0.4388 + i 0.2385#

To divide #(1 +4 i) / (3 - 8i)# using trigonometric form.

#z_1 = (1 +4 i), z_2 = (3 - 8i)#

#r_1 = sqrt(4^2 + 1^2) = sqrt 17

#r_2 = sqrt(3^2 + -8^2) = sqrt 73#

#theta_1 = arctan (4/1) = 75.96^@, " I quadrant"#

#Theta_2 = arctan(-8/3) = 290.56^@, " 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(17/73) * (cos (75.96 - 290.56 ) + i sin (75.96 - 290.56 ))#

#z_1 / z_2 = 0.4826 * (cos (-204.6) + i sin (-204.6))#

#color(blue)((1 + 4i) / (3 - 8i) ~~ 0.4388 + i 0.2385#