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

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Answer 1 · 2018-07-08T03:51:54

#color(green)(=> 026 - 0.18 i)#

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

#z_1 = 2 - i 3, z_2 = 7 - i#

#r_1 = sqrt(2^2 + -1^2) = sqrt 5#

#theta_1 = tan ^ (-1) (-1/2) = 333.43 ^@, " IV Quadrant"#

#r_2 = sqrt(7^2 + (-1)^2) = sqrt 50#

#theta_2 = tan ^-1 (-1/ 7) = 303.69^@, " IV Quadrant"#

#z_1 / z_2 = sqrt(5/50) (cos (333.43- 351.87) + i sin (333.43- 351.87))#

#color(green)(=> 026 - 0.18 i)#