Question

一道高中复数四则运算题目我不太懂,

Answer 1

x^2+xy+y^2=0

x^2=-y(x+y)

y^2=-x(x+y)

所以x/(x+y)=-y/x

y/(x+y)=-x/y

而(x/y)^2+x/y+1=0

所以(x/y)^3=1

同样(y/x)^3=1`

所以[x/(x+y)]^2010+[y/(x+y)]^2010

=(-y/x)^2010+(-x/y)^2010

=[(-y/x)^3]^670+[(-x/y)^3]^670

=[-1]^670+[-1]^670

=1+1

=2