Question

As we know that
( (a+b)(a-b)=a^{2}-b^{2} )
Therefore
( ((x+1)+i)((x+1)-i)(b(-)-i)((x-1)+i) )
( left((x+1)^{2}-i^{2}right)left((x-1)^{2}-i^{2}right) )
( left((x+1)^{2}+1right)left((x-1)^{2}+1right) )
( left((x+1)^{2}+1right)left((x-1)^{2}+1right) )
( left(x^{2}+1+2 x+1right)left(x^{2}+1-2 x+1right) )
( left(left(x^{2}+2right)+2 xright)left(left(x^{2}+2right)-2 xright) )
( left(left(x^{2}+2right)^{2}-(2 x)^{2}right) )
( =x^{4}+4+4 x^{2}-4 x^{2} )
( =x^{4}+9 )
( =R cdot H cdot S )

# 14. Ifi= -1, prove the following: (x + 1 + i)(x + 1 - i)(x - 1 - i)(x - 1 + i) = x +4.

Solution