How do you multiply # (-2-9i)(-1-6i) # in trigonometric form?

Question

1403 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-08T02:54:45

#color(chocolate)((-2 - 9i) / (-1 - 6i) = -50.66 - 24.06)#

#z_1 * z_2 = (|r_1| * |r_2|) (cos (theta_1 + theta_2) + i sin (theta_1 + theta_2))#

#z_1 = -2 - 9i , z_2 = -1 - 6i #

#|r_1| = sqrt(-2^2 + -9^2) = sqrt 85#

#theta_1 = tan ^ (-1) (-9/-2) = 254.05 ^@ " III Quadrant"#

#|r_2| = sqrt(-1^2 + (-6)^2) = sqrt 37#

#theta_2 = tan ^-1 (-6/ -1) = 260.54^@ , " III Quadrant"#

#z_1 / z_2 = |sqrt(85*37)| * (cos (254.05 + 260.54) + i sin (254.05 + 260.54))#

#color(chocolate)((-2 - 9i) / (-1 - 6i) = -50.66 - 24.06)#