How do you divide # (-1+4i)/(3-7i) # in trigonometric form?

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Answer 1 · 2018-07-30T03:17:20

#color(violet)(=> -0.5345 + 0.0862 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 + 4i, z_2 = 3 - 7 i#

#r_1 = sqrt(-1^2 + 4^2)^2) = sqrt 17#

#theta_1 = tan ^-1 (4/ -1) 104.0362^@ , " II Quadrant"#

#r_2 = sqrt(3^2 + (-7)^2) = sqrt 58#

#theta_2 = tan ^-1 (-7/ 3) ~~ 293.1986^@, " IV Quadrant"#

#z_1 / z_2 = sqrt(17 / 58) (cos (104.0362 - 293.1986) + i sin (104.0362 - 293.1986))#

#color(violet)(=> -0.5345 + 0.0862 i, " II Quadrant"#