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

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Answer 1 · 2018-06-25T04:41:25

$color(brown)((3 - i)/ (4 + 2 i) = 1.16 * (0.9532 - i 0.3022)$

$z-1 / z_2 = (r_1 * r_2) * ((cos (theta_1 - theta_2) + i sin (theta_1 - theta_2))$

$z_1 = 7 + i, z_2 = -6 + i$

$r_1 = sqrt(7^2 + 1^2) = sqrt50$

$theta _ 1 = tan ^ -1 (7/1) = 81.87^@, " I quadrant"$

$r_2 = sqrt(-6^2 + 2^2) = sqrt37$

$theta _ 2 = tan ^ -1 (-6/1) = 99.46^@, " II quadrant"$

$z_1 / z_2 = sqrt(50/37) * (cos (81.87 - 99.46) + i (81.87 - 99.46))$

$color(brown)((3 - i)/ (4 + 2 i) = 1.16 * (0.9532 - i 0.3022)$

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