How do you divide #(i+2) / (9i+4)# in trigonometric form?

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Answer 1 · 2018-06-14T03:17:01

#color(blue)((2 + i) / (4 + i9) = 0.175 - i 0.144#

To divide #(2 + i) / (4 + i9)# using trigonometric form.

#z_1 = (2 + i), z_2 = (4+ i9)#

#r_1 = sqrt(2^2 + 1^2) = sqrt5#

#r_2 = sqrt(9^2 + 4^2) = sqrt97#

#theta_1 = arctan (1/2) = 26.57^@#

#Theta_2 = arctan(9/4) = 66.06^@#

#r_1 / r_2 = sqrt 5 * / sqrt 97 ~~ 0.227#

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

#z_1 / z_2 = (0.227) * (cos (26.57 - 66.06 ) + i sin (26.57 - 66.06 ))#

#z_1 / z_2 = 0.227 * (cos (-39.49) + i sin (-39.49)) = 0.227 (0.772 - i 0.636)#

#color(blue)((2 + i) / (4 + i9) = 0.175 - i 0.144#