How do you write the following in trigonometric form and perform the operation given #(1+sqrt3i)/(6-3i)#? Trigonometry The Polar System The Trigonometric Form of Complex Numbers 1 Answer sankarankalyanam Jul 17, 2018 #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)# Answer link Related questions What is The Trigonometric Form of Complex Numbers? How do you find the trigonometric form of the complex number 3i? How do you find the trigonometric form of a complex number? What is the relationship between the rectangular form of complex numbers and their corresponding ... How do you convert complex numbers from standard form to polar form and vice versa? How do you graph #-3.12 - 4.64i#? Is it possible to perform basic operations on complex numbers in polar form? What is the polar form of #-2 + 9i#? How do you show that #e^(-ix)=cosx-isinx#? What is #2(cos330+isin330)#? See all questions in The Trigonometric Form of Complex Numbers Impact of this question 215 views around the world You can reuse this answer Creative Commons License