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This is part of a series on common misconceptions.
True or False?
Why some people say it's true: Subtract from both sides, and we will have , which is obviously true.
Why some people say it's false: (Explanation)
The statement is .
Let's assume it's true, i.e.
Squaring both sides gives which on further simplification gives
Dividing by 2 throughout gives
Squaring LHS and RHS again, we have which gives
This is clearly false, hence a contradiction to our original statement.
Therefore, the given statement is false.
Rebuttal: This doesn’t make sense.
Reply: Imaginary numbers don’t operate in the same way as real numbers