若w=-1/2+根号3/2i,则(1+i/1-i)^2008+1+w=
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![若w=-1/2+根号3/2i,则(1+i/1-i)^2008+1+w=](/uploads/image/z/1121595-51-5.jpg?t=%E8%8B%A5w%3D-1%2F2%2B%E6%A0%B9%E5%8F%B73%2F2i%2C%E5%88%99%EF%BC%881%2Bi%2F1-i%EF%BC%89%5E2008%2B1%2Bw%3D)
若w=-1/2+根号3/2i,则(1+i/1-i)^2008+1+w=
若w=-1/2+根号3/2i,则(1+i/1-i)^2008+1+w=
若w=-1/2+根号3/2i,则(1+i/1-i)^2008+1+w=
[(1+i)/(1-i)]^2=(1+i)^2/(1-i)^2
=(1+2i-1)/(1-2i-1)
=2i/(-2i)
=-1
∴[(1+i)/(1-i)]^2008=1
原式=2+W=(3+根号3)/2