How do you divide # (-7-2i) / (5-6i) # in trigonometric form?

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Answer 1 · 2018-07-03T08:38:35

#color(maroon)((7 - 2i) / (5 - 6i) = -0.377 - 0.8524 i#

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

#z_1 = -7 - 2i , z_2 = 5 - 6i #

#|r_1| = sqrt(-7^2 + 2^2) = sqrt 53#

#theta_1 = tan ^ (-1) (-2/-7) = 195.95 ^@ " III Quadrant"#

#|r_2| = sqrt(5^2 + (-6)^2) = sqrt 61#

#theta_2 = tan ^-1 (-6/ 5) = 309.81^@ , " IV Quadrant"#

#z_1 / z_2 = |sqrt(53/61)| * (cos (195.95- 309.81) + i sin (195.95- 309.81))#

#color(maroon)((7 - 2i) / (5 - 6i) = 0.9321 ( -0.4045 - i 0.9145)#