and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
The terms “real” and “imaginary” are a bit misleading. i is a number, just like 1 or 2. There was a time where people didn’t think pi really existed, but we accept it today, and people should accept i the same way. The only reason sqrt(-1) feels so icky is that you’ve grown up with every teacher in school telling you you can’t do that. But given a bored enough mathematician, anything is possible in math! There’s even cases where we choose to define dividing by 0, but these turn out to not be very useful or nice, so we don’t teach them in school.
Imaginary numbers on the other hand are quite useful, so we do teach them in school! They’re really great at representing 2D rotations, so these pop up all the time in electrical engineering and physics. In fact, there’s even a step above complex numbers called quaternions that are good for representing 3D spin, which physicists use a lot. But complex numbers are complicated enough, so we don’t bother teaching quaternions in school.
In general, none of the rules that you learned are “required” in math are actually required, and mathematicians choose to break these rules all the time to see what happens. When this leads to something cool and useful being discovered, we simply change the rules. You may think this would “break” math or the universe, but math is simply a set of rules we *choose*, and we just typically choose the rules that help us describe our universe. i does help describe our universe since it helps us describe rotating things easily, and so we changed our rules to allow this.
Latest Answers