How do you divide # (7+5i)/(1-3i) # in trigonometric form?

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Answer 1 · 2018-07-26T14:53:08

#color(maroon)(=> -0.8 + 2.6 i),# II QUADRANT

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

#z_1 = 7 + 5 i, z_2 = 1 - 3 i#

#r_1 = sqrt(7^2 + 5^2)^2) = sqrt 74#

#theta_1 = tan ^ -1 (5 / 7) = 35.5377^@ = , " I Quadrant"#

#r_2 = sqrt(1^2 + (-3)^2) = sqrt 10#

#theta_2 = tan ^-1 (-3/ 1) ~~ 288.4349^@, " IV Quadrant"#

#z_1 / z_2 = sqrt(74 / 10) (cos (35.5377 - 288.4349) + i sin (35.5377 - 288.4349))#

#color(maroon)(=> -0.8 + 2.6 i),# II QUADRANT