Use de Moivre's Theorem to evaluate. Write the answer in trigonometric form.

Question

(3-i)^8

Answer 1

3 - i = √10(cos(-arccos(3/√10)) + i sin(-arccos(3/√10)) ) (We chose the negative because 3 - i is in quadrant 4.)

Thus, (3-i)^8 = 10000(cos(-8arccos(3/√10)) + i sin(-8arccos(3/√10)) )

-arccos(3/√10)) = -0.321750554396642 = -°18.434948822922

(3-i)^8 = 10000(cos(-8arccos(3/√10)) + i sin(-8arccos(3/√10)) ) =

10000(cos(8*-0.321750554396642) + i sin(-0.321750554396642)) =

10000(cos(-2.57400443517314) + i sin(2.57400443517314)) =

10000(cos(-147.479590583376°) + i sin (147.479590583376°)) =

10000(-.8432 - .5376 i) = -8432 - 5376 i