Where is the error?

Algebra Level 2

I am performing the following steps to prove − 1 = 1 : -1 = 1:

  1. − 1 = i 2 -1 = i^{2}
  2. − 1 = i × i -1=i \times i
  3. − 1 = − 1 × − 1 -1 = \sqrt{-1} \times \sqrt{-1}
  4. − 1 = − 1 × − 1 -1 =\sqrt{-1 \times -1}
  5. − 1 = 1 -1 =\sqrt{1}
  6. − 1 = 1. -1=1.

In which step does the error exist?

1 2 3 4 5 6

Prince Loomba by Prince Loomba , 21, India

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1 solution

Hung Woei Neoh
Jun 13, 2016

a × b = a b if and only if a ≥ 0 or b ≥ 0 \sqrt{a} \times \sqrt{b} = \sqrt{ab} \text{ if and only if } a \geq 0 \text{ or } b \geq 0

Therefore, − 1 × − 1 ≠ − 1 × − 1 \sqrt{-1} \times \sqrt{-1} \neq \sqrt{-1 \times -1} because − 1 < 0 -1 < 0

The error appeared in Step 4 \boxed{4}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Wait, why a a and b b must ≥ 0 \geq 0 ?

Then what is − 9 \sqrt{-9} ? It's suppose to be 3 i 3i

Jason Chrysoprase - 5 years ago

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Oh right, it's supposed to be "or". I've edited it. Thanks

Hung Woei Neoh - 5 years ago

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Ohh make sense, notice you ;)

Jason Chrysoprase - 5 years ago

answer is 4.but result showing 1.i can't understand.

niloy debnath - 5 years ago

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That was an error. It's fixed

Hung Woei Neoh - 5 years ago

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