I may actually read it it sounds fascinating.It's an oft told tale, the idea was come across by Italian mathematicians Tartaglia, Cardano, Bombelli (who actually did what is a complicated story) in the Renaissance, in the 16th century. Arguably the most important peice of math ever done, no one will dispute one of the most.
Complex numbers can now be given a concrete image you probably know and made fairly obvious. Used by engineers and practical people every day. But that was only thought of centuries later. At the time it was just the square root of minus one which "obviously can't exist" but suspending disbelief if it existed they could use it in calculations (namely for solving cubic equations) and get just real number results, it worked! They called it strange names like "less of minus" or something. I think that was the first time they ever worked with such a thing of which there was no concrete model, that makes it quite pathbreaking, and set a new pattern for math, which is why it is so important.
They didn't like having to do it, and for a long time they thought it was a temporary expedient or shortcut, till they could find a more satisfactory way of solving cubics etc. I read it has been proved There Is No Alternative, that hey cannot be avoided in solving cubics and other problems - I don't know how advanced that proof is.
I am writing this from memory but there are loads of books on this history.