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A PowerSum Puzzle (
Posted on 20140827
)
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?
No Solution Yet
Submitted by
Danish Ahmed Khan
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Close but not quite.
 Comment 1 of 3
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 20140831 01:31:59
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