Definition:Imaginary Number/Historical Note

Historical Note on Imaginary Number
was one of the first to accept negative numbers, and possibly the first to consider their square roots, which he did in his.

When considering the roots of $x^2 + 40 = 10 x$, and determining that they are $5 \pm \sqrt {-15}$, he concluded:
 * These quantities are "truly sophisticated" and that to continue working with them would be "as subtle as it would be useless".

As negative numbers were even then considered "false" and "fictitious", no wonder the square roots of negative numbers would be named imaginary.