This is the first book in the series of Althea's Math Mysteries. Althea asks her mom if there's a square root of -1. Mom tells her about some crazy history, and they play with imaginary and complex numbers.
References
My poem, Imaginary Numbers Do the Trick
Journey Through Genius: The Great Theorems of Mathematics, by William Dunham. The history Mom tells comes mainly from Chapter 6, Cardano and the solution of the cubic. (I spent a lot of time online trying to track down many of the details in this story, but it's always possible I have some of the details wrong.)
More on the history:
www-history.mcs.st-and.ac.uk/history/Biographies/Tartaglia.html
maa.org/press/periodicals/convergence/how-tartaglia-solved-the-cubic-equation-the-first-solutions
maa.org/press/periodicals/convergence/mathematical-treasure-cardanos-ars-magna
quora.com/What-were-the-renaissance-mathematics-competitions-in-Italy
math.stackexchange.com/questions/534474/discovery-of-complex-numbers
https://www.quantamagazine.org/the-scandalous-history-of-the-cubic-formula-20220630/
Ars Magna, 1545
Luca Pacioli invented double entry bookkeeping.
More on complex numbers:
math.stackexchange.com/questions/1078618/easy-example-why-complex-numbers-are-cool
mikesmathpage.wordpress.com/2016/05/25/a-great-complex-number-question-from-art-of-problem-solving/
Youtube: Imaginary Numbers are Real (This is part 1 of 13 parts.)
Excellent summary, includes much of what is discussed in the book
Dividing by a factor to get a simpler equation (discussed on page 41)
Radiolab Podcast on division by zero (about 8 minutes in for the part on imaginary numbers)
Quadratic Reciprocity is a strange tool in number theory that got generalized to a tool using complex numbers