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
There is a great variety of good answers here already, I’ll address a different part of your questioning.
> I can’t tell if [imaginary numbers] exist just to make math work better
Do negative numbers such as `-1` or `-⅓` exist or are they just to make math work better? There is no way I can hold “-5 acorns” in my hand, it’s not found in nature. An expression such as `3 + 6 = ?` is fine, as well as `6½ – 3 = ?` but `3 – 6 = ?` is absurd and can’t have a solution, can it?
As you already know, humans eventually came up with negative numbers; they have no “natural” correspondence, they are a concept, and a very useful one; they make all subtractions of rational numbers possible. Think again about it, do negative numbers exist or are they just to make math work better?
Imaginary numbers make roots of all rational numbers possible, not just a subset of them — similar story to negative numbers. Is `√-1 (i)` that much more “removed from the real world” than negative numbers?
Latest Answers