To divide (-3 - 5 i)* (1 - 16 i)(−3−5i)⋅(1−16i) using trigonometric form.
z_1 = (-3 - 5 i), z_2 = (1 - 16 i)z1=(−3−5i),z2=(1−16i)
#r_1 = sqrt(-3^2 + 5^2) = sqrt 34
r_2 = sqrt(1^2 + -16^2) = sqrt 257r2=√12+−162=√257
theta_1 = arctan (-5/-3) = 239.04^@, " III quadrant"θ1=arctan(−5−3)=239.04∘, III quadrant
Theta_2 = arctan(-16/1) = 273.58^@, " IV 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(34/257) * (cos (239.04 + 273.58 ) + i sin (239.04 + 273.58 ))
z_1 / z_2 = sqrt(34/257) * (cos (512.62) + i sin (512.62))
color(brown)((-3 - 5 i) * (1 - 16 i) ~~ -0.323 + i 0.1673