@ZachWeinersmith If you're introducing it, I would start with a number line. Explain that all real numbers are there. Now show them that sqrt(-1) is not there. Now, assuming that's a number at all, you can multiply that number by any real number and you get a second number line. 1i, 2i, 3i, etc ... EXCEPT 0 times anything is 0. So those two points have to be the same. That's when you erase the second number line and make it vertical. THAT'S where your complex plane comes from.