Dave wrote:

I have to confess that I never understood what the square root of -1
was.

"i" or "j" depending on whose notation you want...

... The product of what times itself will equal -1?

"i" or "j" ... think of it simply as "by definition" that j*j = -1 and
anywhere you need it you make the substitution and carry on...leads to
the expansion of the "real" numbers to include the "complex" numbers of
the form "a +/- jb", for 2 + 3j. Rules for things like
addition/subtraction are add real and imaginary parts separatel,
multiplication is like algebraic...

(2+3j)*(1+2j) = 2*1 + (2*2j+3j*1) + 2j*3j
= 2 + 7j + 6j**2
= 2 + 7j + 6*(-1)
= 2-6 + 7j
= -4 + 7j

Clear as mud? Notice all that was done in last simplification was
to associate terms and substitute -1 for the j-squared term.