1.若f(a)=2a+ā-3i,f(ā+i)=6-3i,则f(-a)=2.若x+1/x=-1,则x^2007+1/x^2007=

Question

1.若f(a)=2a+ā-3i,f(ā+i)=6-3i,则f(-a)=
2.若x+1/x=-1,则x^2007+1/x^2007=

Answer 1

1.设:a=x+yi,(x,y属于R)所以ā=x-yi.所以ā+i共轭复数为:x-(1-y)i
f(ā+i)=2(x-yi+i)+x-(1-y)i-3i=3x-(y+1)i=6-3i
复数相等充要条件知:3x=6,y+1=3,解得:x=y=2,
a=2+2i,-a=-2-2i
f(-a)=-2(-2-2i)+(-2+2i)-3i=2+3i
2.解方程x+1/x=-1得:x=-1/2±[(√3)/2]i
可知x^3n=1,(n属于N)
所以x^2007+1/x^2007=x^3*669+1/x^3*669=1+1=2