Imaginary numbers

Question

I am going into Honors Algebra II and while I am fine at using imaginary numbers in a formulaic sense I never understood them conceptually. I can’t tell if they exist just to make math work better or because there is an actual logical way to understand them

In: 16

Answer 1

Imaginary numbers are cook. Think about it. i^4 = 1 so under multiplication i 1 and negation operator make a closed algebraic group.