How do you divide # (7+8i) / (2+i) # in trigonometric form?

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Answer 1 · 2018-08-01T07:25:26

#color(indigo)(=> 4.4 + 1.8 i, " I Quadrant"#

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

#z_1 = 7 + 8 i, z_2 = 2 + i#

#r_1 = sqrt(7^2 + 8^2)^2) = sqrt 113#

#theta_1 = tan ^-1 (8/ 7) = 48.8141^@ , " I Quadrant"#

#r_2 = sqrt(2^2 + (1)^2) = sqrt 5#

#theta_2 = tan ^-1 (1/ 2) ~~ 26.5651^@, " I Quadrant"#

#z_1 / z_2 = sqrt(113 / 5) (cos (48.8141 - 26.5651) + i sin (48.8141 - 26.5651))#

#color(indigo)(=> 4.4 + 1.8 i, " I Quadrant"#