Complex Number Paradox

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement.


The reason for the fallacy is that sqrt(-1) is not an ordinary (real) square root, hence the rule for computing the quotient of radicals does not apply to it.

This entry contributed by Margherita Barile

Explore with Wolfram|Alpha


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.

Referenced on Wolfram|Alpha

Complex Number Paradox

Cite this as:

Barile, Margherita. "Complex Number Paradox." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications