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

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Answer 1 · 2018-06-25T05:07:47

#color(green)((10 - 2 i)* (3 - i) = 18.44 * (-0.9762 - i 0.217)#

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

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

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

#theta _1 = tan ^-1 (-3/-5) = 210.96^@, " III quadrant"#

#r_2 = sqrt (3^2 + -1^2) = sqrt (10)#

#theta _2 = tan ^-1 (-1/3) = -18.43^@ = 341.57^@, " IV quadrant"#

#z_1 * z_2 = (sqrt34 * sqrt 10) * (cos(210.96 + 341.57) + i (210.96 + 341.57))#

#color(green)((10 - 2 i)* (3 - i) = 18.44 * (-0.9762 - i 0.217)#