设函数f(x)=-x5+5x4-10x3+10x2-5x+1,则f(12+32i)的值为( ) A.-12+32i B.32-12i C.12+32i D.-32+12i
问题描述:
设函数f(x)=-x5+5x4-10x3+10x2-5x+1,则f(
+1 2
i)的值为( )
3
2
A. -
+1 2
i
3
2
B.
-
3
2
i1 2
C.
+1 2
i
3
2
D. -
+
3
2
i 1 2
答
∵f(x)=-(x-1)5
∴f(
+1 2
i)=-(
3
2
+1 2
i-1)5
3
2
=-ω5(其中ω=-
+1 2
i)
3
2
=-(-
-1 2
i)5=
3
2
+1 2
i
3
2
故选B.