This problem requires advanced algebra (imaginary numbers). Let the symbol 'Sqrt(x)' stand for "the square root of x," and let the symbol 'i' stand for the unit imaginary number, whose square is equal to -1, and let 'x^y' stand for "x raised to the yth power." We can show that -1 is equal to 1:
1 i = i Trivial 2 i^2 = i^2 Square both sides 3 i^2 = i*i Expand the definition of i^2 4 (Sqrt(-1))^2 = Sqrt(-1)*Sqrt(-1) Expand the defintion of i 5 (Sqrt(-1))^2 = Sqrt(-1 * -1) Rule: Sqrt(x)*Sqrt(y) = Sqrt(x*y) 6 -1 = Sqrt(-1 * -1) Rule: Sqrt(x)^2 = x 7 -1 = Sqrt(1) The product of -1 and -1 is 1 8 -1 = 1 The square root of 1 is 1What is wrong with this reasoning?