(1+√3i)^2 = 1-3 + 2√3i = -2 (1-√3i)
(1-√3i)^2 = 1-3 - 2√3i = -2 (1+√3i)
(1+√3i)^3 = -2(1-√3i)*(1+√3i) = -2 * ( 1+4)=-2^3
(1-√3i)^3 = -2(1+√3i)*(1-√3i) = -2 * ( 1+4)=-2^3
因此
（1+√3i)^100+(1-√3i)^100
= （1+√3i)^99*（1+√3i） + (1-√3i)^99*（1-√3i）
= -2^99 * (1+√3i) - 2^99*(1-√3i)
= -2^99 * ( 1+1+√3i-√3i )
= -2^100