Suppose a, b, c, d are complex numbers such that

a + b + c + d = 1
a^2 + b^2 + c^2 + d^2 = 0
a^3 + b^3 + c^3 + d^3 = 1
a^4 + b^4 + c^4 + d^4 = 0

What is a^10 + b^10 + c^10 + d^10?

In polar form with r=cos(3pi/8)
a = r cis(pi/8)
b = r cis(3pi/8)
c = r cis(-pi/8)
d = r cis(-3pi/8)

a + b + c + d = 1
a^2 + b^2 + c^2 + d^2 = 0
a^3 + b^3 + c^3 + d^3 ≈ -.06066
a^4 + b^4 + c^4 + d^4 = 0

Posted by Jer on 2014-08-31 01:31:59