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

I tend to look at them as another batch of numbers, orthogonal to the standard set of real numbers we have. So to map one to the other we multiply by i. Multiply by i again and we map them back to the real numbers (negated, because we’re essentially rotating 90 degrees each time)