Problem: If f(x)=x4+x2x+1f(x)=\dfrac{x^{4}+x^{2}}{x+1}f(x)=x+1x4+x2, then f(i)f(i)f(i), where i=−1i=\sqrt{-1}i=−1, is equal to
Answer Choices:
A. 1+i1+i1+i
B. 111
C. −1-1−1
D. 000
E. −1−i-1-i−1−i Solution:
Since i2i^{2}i2 and i4i^{4}i4 are -1 and 1,f(i)=(1−1)/(1+i)=0/(1+i)=01, f(i)=(1-1) /(1+i)=0 /(1+i)=01,f(i)=(1−1)/(1+i)=0/(1+i)=0.