An imaginary error?

Algebra Level 3

The following is my attempt at proving that \(1 < -1\). In which of these steps did I first make a mistake by using flawed logic?

Step 1: Let \(i = \sqrt{-1} \), then \(i^2 = -1\) and \(i^4 = \big(i^2\big)^2 = (-1)^2 = 1\).

Step 2: Hence, we have \(i^2 < i^4 \).

Step 3: We divide both sides by \(i\) to get \(i < i^3\).

Step 4: We divide both sides by \(i\) again to get \(1 < i^2 \) or, equivalently, \(1 < -1 \).

×

Problem Loading...

Note Loading...

Set Loading...