Among the other feats of the Ars magna there was the first use of
complex numbers that ever entered a treatise of algebra. It is true that
Cardano himself considered them as arithmetic subtleties which were as refined
as useless, but he nonetheless has the credit for having at least considered
them. They are mentioned in the 
chapter: find two number whose sum is
10 and whose product is 40. Now, 
and 
.