SOLUTION: Simplify the following and give the answer in the form a+bi. (1 - i)^8 (use Euler form). Thanks in advance.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Simplify the following and give the answer in the form a+bi. (1 - i)^8 (use Euler form). Thanks in advance.      Log On


   

Question 221232: Simplify the following and give the answer in the form a+bi.
(1 - i)^8 (use Euler form).
Thanks in advance.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(1 - i)^8
r = sqrt(2)
theta = -45º
z = rcis(theta) = sqrt(2)cis(-45)
z^8 = (sqrt(2))^8cis(-45*8)
z^8 = 16cis(-360)
z^8 = 16(cos(360) + isin(360)) (+360 = -360)
z^8 = 16