To divide (-5 - 7 i) / (-2 +9 i) using trigonometric form.
z_1 = (-5 - 7 i), z_2 = (-2 +9 i)
#r_1 = sqrt(-5^2 - 7^2) = sqrt 74
r_2 = sqrt(-2^2 + 9^2) = sqrt 85
theta_1 = arctan (-5/-7) = 215.54^@, " III quadrant"
Theta_2 = arctan(-2/9) = 167.47^@, " II 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(74/85) * (cos (215.54 - 167.47 ) + i sin (215.54 - 167.47 ))
z_1 / z_2 = sqrt(74/85) * (cos (48.07) + i sin (48.07))
color(chocolate)((-5 - 7 i) / (-2 +9 i) ~~ 0.6235 + i 0.6942