An improper use of the symbol 
for the imaginary unit
leads to the apparent proof of a false statement.
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.
This entry contributed by Margherita
Barile
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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.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. https://mathworld.wolfram.com/ComplexNumberParadox.html
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