How do you divide # (8+7i)/(1-5i) # in trigonometric form?

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Answer 1 · 2018-06-15T04:49:37

#color(brown)(=> 2.08 (-0.5014 + i 0.787)#

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

#z_1 = 8 + i 7, z-2 = 1 - i 5#

#r_1 = sqrt(8^2 + 7^2) = sqrt113#

#theta_1 = arctan (7/6) = 49.4^@#

#r_2 = sqrt(1^2 + 5^2) = sqrt26#

#theta_2 = arctan (-5/1) = 281.31^@, " IV Quadrant" #

#z_1 / z_2 = sqrt(113/26) (cos (49.4 - 281.31) + i sin(49.4 - 281.31)#

#color(brown)(=> 2.08 (-0.5014 + i 0.787)#