2=0?

Algebra Level 3

In the proof below, in which step does the first mistake occur?

  • Step 1. \(\ 2 = 1 + 1\)
  • Step 2. \(\ 2 = 1 + \sqrt{1}\)
  • Step 3. \(\ 2 = 1 + \sqrt{(-1)(-1)}\)
  • Step 4. \(\ 2 = 1 + \sqrt{(-1)}\)\(\sqrt{(-1)}\)
  • Step 5. \(\ 2 = 1 + (i)(i)\)
  • Step 6. \(\ 2 = 1 + (-1)\)
  • Step 7. \(\ 2 = 0\)
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