"Proof" that 1 = –1

We use the complex number *i* which has the property
*i*² = –1

we know that (–1)(–1) = 1

taking the square root of both sides preserves the equality, and we get:

1 = sqrt[1] = sqrt[(–1)(–1)] = sqrt[–1]sqrt[–1] =

i·i=i²= –1hence 1 = –1

Can this be correct? Obviously not. Hint: consider the quadratic polynomial
(*x*²+1).

This apparent "paradox" can be easily explained: see solution. **But hold on**, before you dismiss it as
completely trivial, it does lead to some further rather interesting
mathematics, as is indicated at the end of the solution section.