How do you divide #( -2i+7) / ( -8i -3 )# in trigonometric form?

Question

1281 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-15T04:22:33

#color(indigo)(=> 0.85 (-0.0804 + i 0.9968)#

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

#z_1 = 7 - i 20, z _2 = (-3 - i 8)#

#r_1 = sqrt(7^2 +2^2) = sqrt53#

#Theta_1 = arctan (-2/7) = 344.05^@, " IV Quadrant"#

#r_2 = sqrt(8^2 +3^2) = sqrt73#

#Theta_2 = arctan (-8/ -3) = 249.44^@, " III Quadrant"#

#z_1 / z_2 = (sqrt53 / sqrt73) (cos (344.05 - 249.44) + i sin(344.05 - 249.44))#

#color(indigo)(=> 0.85 (-0.0804 + i 0.9968)#