Compute x2+ 2/x2 where x=i−1

x2-2x2

#1

Compute x2+ 2/x2 where x=i−1.

Answer:

x^2 + 2/ x^2
=(i -1)^2 + 2/(i-1)^2
={ (i-1)^2 * (i-1)^2 + 2 } / (i - 1)^2
={ ( i^2 - 2i + 1) * (i^2 - 2i +1) + 2}/ (i^2 - 2i + 1)
={ (-2i) * (-2i) + 2 }/ (-2i) //since i=sqrt(-1), so i^2= -1;
={ 4 i^2 + 2}/(-2i)
=(-4 + 2)/(-2i)
=(-2)/(-2i)
=1 / i ;