How do you write the following in trigonometric form and perform the operation given #-2i(1+i)#?

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Answer 1 · 2018-07-09T11:18:25

#color(purple)(-2i * (1 + i) = 2 - 2 i)#

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

#z_1 = 0 - 2 i, z_2 = 1 + i#

#r_1 = sqrt(0^2 + -2^2) = 2#

#theta_1 = tan ^ (-1) (-2/0) = 270 ^@, " IV Quadrant"#

#r_2 = sqrt(1^2 + (1)^2) = sqrt 2#

#theta_2 = tan ^-1 (1/ 1) = 45^@, " I Quadrant"#

#z_1 * z_2 = (2*sqrt(2)) (cos (270 + 45) + i sin (270 + 45))#

#color(purple)(-2i * (1 + i) = 2 - 2 i)#