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

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Answer 1 · 2018-06-28T04:28:37

#color(maroon)((-1 + 3i) / (3 - 8i) ~~ -0.3666 - i 0.0508#

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

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

#r_1 = sqrt(3^2 + 1^2) = sqrt 10

#r_2 = sqrt(87^2 + -3^2) = sqrt 73#

#theta_1 = arctan (-3/1) = 108.43^@, " II 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(10/53) * (cos (108.43 - 290.56 ) + i sin (108.43 - 290.56 ))#

#z_1 / z_2 = sqrt910/53) * (cos (-172.13) + i sin (-172.13))#

#color(maroon)((-1 + 3i) / (3 - 8i) ~~ -0.3666 - i 0.0508#