How do you divide #( -i+4) / (2i +7 )# in trigonometric form?

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Answer 1 · 2018-06-28T04:16:36

#color(violet)((4 -i) / (7 + 2i) ~~ 0.4905 + i 0.2831#

To divide #(4 - i) / (7 + 2i)# using trigonometric form.

#z_1 = (4 - i), z_2 = (7 + 2i)#

#r_1 = sqrt(4^2 + 1^2) = sqrt 17

#r_2 = sqrt(7^2 + -2^2) = sqrt53#

#theta_1 = arctan (-1/4) = 345.96^@, " IV quadrant"#

#Theta_2 = arctan(2/7) = 15.95^@, " I quadrant"#

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

#z_1 / z_2 = sqrt(17/53) * (cos (345.96 - 15.95 ) + i sin (345.96 - 15.95 ))#

#z_1 / z_2 = 0.5664 * (cos (-330.01) + i sin (-330.01))#

#color(violet)((4 -i) / (7 + 2i) ~~ 0.4905 + i 0.2831#