How do you divide #( i-1) / (-i +10 )# in trigonometric form?

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Answer 1 · 2018-07-28T11:50:03

#color(indigo)(=> -0.1089 + 0.0891 i, " II Quadrant"#

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

#z_1 = -1 + i, z_2 = 10 - i#

#r_1 = sqrt(-1^2 + 1^2)^2) = sqrt 2#

#theta_1 = tan ^-1 (1/ -1) 135^@ , " II Quadrant"#

#r_2 = sqrt(10^2 + (-1)^2) = sqrt 101#

#theta_2 = tan ^-1 (-1/ 10) ~~ 354.29^@, " IV Quadrant"#

#z_1 / z_2 = sqrt(2 / 101) (cos (135 - 354.29) + i sin (135 - 354.29))#

#color(indigo)(=> -0.1089 + 0.0891 i, " II Quadrant"#