非零复数a,b满足a^2+ab+b^2=0,则（a/(a+b))^1999+（b/(a+b))^1999的值是?
问题描述：
非零复数a,b满足a^2+ab+b^2=0,则（a/(a+b))^1999+（b/(a+b))^1999的值是?
答
复数a,b非零,且a^2 + ab + b^2 = 0,所以,(a+b)^2 = aba/(a+b) = (a+b)/b = [b/(a+b)]^(-1) ...（1）又,a/(a+b) + b/(a+b) = 1 ...（2）令 u = a/(a+b),则由（1）和（2）解得,a/(a+b) = u = (1 + i(3)^(1/2))/2= exp[...