How do you divide #(4i-5) / (7i+3)# in trigonometric form?

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Answer 1 · 2018-06-24T05:55:40

#color(brown)(=> 0.8408 ( 0.3 - i 0.9539)#

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

#z_1 = -5 + i 4, z_2 = 3 + i 7#

#r_1 = sqrt(5^2 + 4^2) = sqrt 41#

#theta_1 = tan ^ (-1) (4/-5) = tan ^-1 (-0.8) = -38.66 ^@ = 141.34, " II Quadrant"#

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

#theta_2 = tan ^-1 (7/ 3) = 68.8^@#

#z_1 / z_2 = sqrt(41/58) (cos (141.34- 68.8) - i sin (141.34 - 68.8))#

#color(brown)(=> 0.8408 ( 0.3 - i 0.9539)#