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) #