How do you divide # (9+2i) / (5-6i) # in trigonometric form?

Question

1225 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-25T01:46:28

#color(maroon)((9 + 2i) / (5-6i) = 1.18 ( 0.611 + i 0.7917)#

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

#z_1 = 9 + 2 i , z_2 = 5 - 6 i #

#r_1 = sqrt(9^2 + 2^2) = sqrt 85#

#theta_1 = tan ^ (-1) (2/9) = 12.53 ^@ " I Quadrant"#

#r_2 = sqrt(5^2 + (-67)^2) = sqrt 61#

#theta_2 = tan ^-1 (-6/ 5) = -39.81^@ = 320.19, " IV Quadrant"#

#z_1 / z_2 = sqrt(85/61) (cos (12.53- 320.19) + i sin (12.53 - 320.19))#

#color(maroon)((9 + 2i) / (5-6i) = 1.18 ( 0.611 + i 0.7917)#