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.

The strict result for using the radical symbol as a principle square root is:

Edited on June 27, 2023, 2:45 am

Posted by Steven Lord on 2023-06-26 09:47:35