How do you divide #( 3i +7) / (- 7 i + 8 )# in trigonometric form?

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Answer 1 · 2018-06-24T05:48:06

#color(maroon)(=> 0.7164 ( -0.3138 + i 0.9495)#

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

#z_1 = 7 + i 3, z_2 = 8 - i 7#

#r_1 = sqrt(7^2 + 3^2) = sqrt 58#

#theta_1 = tan ^ (-1) (7/3) = 66.8 ^@#

#r_2 = sqrt(8^2 + (7)^2) = sqrt 113#

#theta_2 = tan ^-1 (-7/ 8) = -41.19^@ = 318.51^@, " IV Quadrant"#

#z_1 / z_2 = sqrt(58/113) (cos (66.8- 318.51) + i sin (66.8- 318.51))#

#color(maroon)(=> 0.7164 ( -0.3138 + i 0.9495)#