How do you write the following in trigonometric form and perform the operation given #(1+sqrt3i)/(6-3i)#?

1 Answer
Jul 17, 2018

Answer:

#color(green)(=> 0.0178 + 0.2976 i)#

Explanation:

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

#z_1 = 1 + 3 i, z_2 = 6 - 3 i#

#r_1 = sqrt(1^2 + sqrt3^2) = 2#

#theta_1 = tan ^ (sqrt3)/ (1) = 60^@ ^@, " I Quadrant"#

#r_2 = sqrt(6^2 + (-3)^2) = sqrt 45#

#theta_2 = tan ^-1 (-3/ 6) ~~ 333.43^@, " IV Quadrant"#

#z_1 / z_2 = 2/sqrt(45) (cos (60- 333.43) + i sin (60- 333.43))#

#color(green)(=> 0.0178 + 0.2976 i)#