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

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