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

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Answer 1 · 2018-07-17T07:37:43

$color(blue)(=> 0.064 - 0.048 i)$

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

$z_1 = 2 - 2 i, z_2 = 7 - i$

$r_1 = sqrt(2^2 + _-2)^2) = sqrt8$

$theta_1 = tan ^ (-2)/ (2) = -45^@ = 315^@, " IV Quadrant"$

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

$theta_2 = tan ^-1 (-1/ 7) ~~ 351.87^@, " IV Quadrant"$

$z_1 / z_2 = sqrt(8/50) (cos (315- 351.87) + i sin (315- 351.87))$

$color(blue)(=> 0.064 - 0.048 i)$

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