How do you multiply # (3+9i)(5+4i) # in trigonometric form?

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Answer 1 · 2018-06-25T04:54:56

# color(indigo)((3 + 9 i)* (5 + 4i) = 60.75 * (-0.3458 + i 0.9383)#

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

#z_1 = (3 + 9 i), z_2 = (5 + 4i)#

#r_1 = sqrt (3^2 + 9^2) = sqrt (90)#

#theta _1 = tan ^-1 (9/3) = 71.57^@, " I quadrant"#

#r_2 = sqrt (4^2 + 5^2) = sqrt (41)#

#theta _2 = tan ^-1 (4/5) = 38.66^@, " I quadrant"#

#z_1 * z_2 = sqrt90 * sqrt 41) * (cos(71.57 + 38.66) + i (71.57 + 38.66))#

# color(indigo)((3 + 9 i)* (5 + 4i) = 60.75 * (-0.3458 + i 0.9383)#