How do you use DeMoivre's theorem to simplify (1+i)^4?
1 Answer
Sep 11, 2016
Explanation:
Note that
1+i = sqrt(2)(cos (pi/4) + i sin (pi/4))
De Moivre tells us that:
(cos theta + i sin theta)^n = cos n theta + i sin n theta
So we find:
(1+i)^4 = (sqrt(2)(cos (pi/4) + i sin (pi/4)))^4
color(white)((1+i)^4) = (sqrt(2))^4(cos (pi/4) + i sin (pi/4))^4
color(white)((1+i)^4) = 4(cos pi + i sin pi)
color(white)((1+i)^4) = 4((-1) + i (0))
color(white)((1+i)^4) = -4
