How do you multiply # (3-5i)(1-16i) # in trigonometric form?

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Answer 1 · 2018-07-08T01:52:59

#color(brown)((-3 - 5 i) * (1 - 16 i) ~~ -0.323 + i 0.1673#

To divide #(-3 - 5 i)* (1 - 16 i)# using trigonometric form.

#z_1 = (-3 - 5 i), z_2 = (1 - 16 i)#

#r_1 = sqrt(-3^2 + 5^2) = sqrt 34

#r_2 = sqrt(1^2 + -16^2) = sqrt 257#

#theta_1 = 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#