How do you divide #( 3i+8) / (6i +4 )# in trigonometric form?

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Answer 1 · 2018-06-25T06:02:46

#color(purple)((8 + 3i) / (4 + 6i) = 1.1007 ( 0.9731 - i 0.2306)#

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

#z_1 = 8 +3 i , z_2 = 4 + 6 i #

#|r_1| = sqrt(8^2 + 3^2) = sqrt 73#

#theta_1 = tan ^ (-1) (3/8) = 20.56 ^@ " I Quadrant"#

#|r_2| = sqrt(4^2 + (6)^2) = sqrt 52#

#theta_2 = tan ^-1 (4/ 6) = 33.69^@ , " I Quadrant"#

#z_1 / z_2 = |sqrt(63/52)| * (cos (20.56 - 33.69) + i sin (20.56 - 33.69))#

#color(purple)((8 + 3i) / (4 + 6i) = 1.1007 ( 0.9731 - i 0.2306)#