How do you multiply # (1-i)(-4-3i) # in trigonometric form?

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Answer 1 · 2018-07-08T02:29:50

#color(indigo)((1 - i)* (-4 - 3 i) ~~ -0.28 + i 0.04#

To divide #(1 - i)* (-4 - 3 i)# using trigonometric form.

#z_1 = (1 - i), z_2 = (-4 - 3 i)#

#r_1 = sqrt(-1^2 + 1^2) = sqrt 2

#r_2 = sqrt(-3^2 + -4^2) = 5#

#theta_1 = arctan (-1/1) = 315^@, " IV quadrant"#

#Theta_2 = arctan(-3/-4) = 216.87^@, " III quadrant"#

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

#z_1 / z_2 = sqrt2 / 5 * (cos (315 + 216.87 ) + i sin (315 + 216.87 ))#

#z_1 / z_2 = sqrt2 / 5 * (cos (531.87) + i sin (531.87))#

#color(indigo)((1 - i)* (-4 - 3 i) ~~ -0.28 + i 0.04#