Complex numbers ≠ Imaginary numbers

the name seems to be an unfortunate choice that stems from their historical usage as “a means to an end”. i.e, they were first used as part of a method to find some solutions to cubic equations. this method would require algebraic manipulations of complex numbers, but the ultimate goal was to discover a real root. the complex roots would be discarded once a real root was found (if it existed).

the wikipedia article attributes the name to Descartes:

… sometimes only imaginary, that is one can imagine as many as I said in each equation, but sometimes there exists no quantity that matches that which we imagine.

which i think helps to highlight how skeptical the people at that time were about the existence of the “imaginary” numbers.

source: memories of my first complex analysis class, and https://en.wikipedia.org/wiki/Complex_number#History

i’d strongly recommend reading the history section of that wikipedia page to anyone interested in the topic, it has some pretty fun history

The Italian Bombelli in 1572 seemed to toy with both concepts but called imaginary numbers “quantità silvestri” (silvestri meaning ‘wild’) and complex numbers “numeri complessi”. Interesting the imaginary is a quantity and the complex is a number, but maybe old Italian didn’t have that distinction.

I suppose Descartes would agree with you, he first coined the term “imaginary” because he didn’t think they’d serve much purpose. Euler made use of them and continued using the term. Complex number is a complex - a number with a real and an imaginary component.

Well it's true, they don't exist