Let us consider a positive real number A.

For the imaginary number i, we know that: i*i = -1.

Therefore, i*i*i*i = (-1)*(-1)= 1

Hence, A*i*i*i*i = A

or √(A*i*i*i*i) = √A

or, √(A)*(i*i) = √A,

since sqrt(i*i*i*i) = i*i

or, - √(A) = √(A)

Provide a valid reason for this apparent inconsistency.