复数计算 (1-根号3i)^10-(1+根号3i)^10=?

解析：(1-根号3i)^10=2^10 ×(1/2 -根号3/2 ×i)^10=2^10 ×[cos(-π/3)+sin(-π/3)×i]^10=2^10 ×[cos(-10π/3)+sin(-10π/3)×i]=2^10 ×[cos(2π/3)+sin(2π/3)×i]=2^10 ×（-1/2+根号3/2×i ）而 (1+根号3i)^10=2^10 ×(1/2 +根号3/2 ×i)^10=2^10 ×[cos(π/3)+sin(π/3)×i]^10=2^10 ×[cos(10π/3)+sin(10π/3)×i]=2^10 ×[cos(4π/3)+sin(4π/3)×i]=2^10 ×[-cos(π/3)-sin(π/3)×i]=2^10 ×（-1/2-根号3/2×i ）所以： (1-根号3i)^10-(1+根号3i)^10=2^10 ×（-1/2+根号3/2×i ）－2^10 ×（-1/2-根号3/2×i ）=2^10 ×[（-1/2+根号3/2×i ）-（-1/2-根号3/2×i ）]=2^10 ×根号3×i=1024根号3×i