How do you divide #( 7i+1) / (i -6 )# in trigonometric form?

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Answer 1 · 2018-07-26T15:47:44

#color(crimson )(=> 0.027 - 1.1622 i),# IV QUADRANT

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

#z_1 = 1 + 7 i, z_2 = -6 + i#

#r_1 = sqrt(1^2 + 7^2)^2) = sqrt 50#

#theta_1 = tan ^ -1 (7 / 1) = 81.8699^@ = , " I Quadrant"#

#r_2 = sqrt(-6^2 + (1)^2) = sqrt 37#

#theta_2 = tan ^-1 (1/ -6) ~~ 170.5377^@, " II Quadrant"#

#z_1 / z_2 = sqrt(50 / 37) * (cos (81.8699 - 170.5377) + i sin (81.8699 - 170.5377))#

#color(crimson )(=> 0.027 - 1.1622 i),# IV QUADRANT