Complex Number Paradox

An improper use of the symbol  for the imaginary unit leads to the apparent proof of a false statement.

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The reason for the fallacy is that  is not an ordinary (real) square root, hence the rule for computing the quotient of radicals does not apply to it.

REFERENCES:

Eves, H. An Introduction to the History of Mathematics, 3rd ed. New York: Holt, Rinehart, and Winston, p. 385, 1969.

Gardner, M. Mathematical Puzzles and Diversions. New York: Simon and Schuster, p. 144, 1959.