I was going to post something like this but you did a much better job of it. In some sense, TLDR: "Imaginary number" is a misnomer that confuses people. 1+2i i

I was going to post something like this but you did a much better job of it. In some sense, TLDR: "Imaginary number" is a misnomer that confuses people. 1+2i is also just a convenient but potentially confusing notation to those who don't know what it is a short-hand for. Complex numbers are basically 2D vectors with a funny multiply operation ((a,b)(c,d) = (ac-bd,bc+ad)) and it just so happens that defining it this way leads to some interesting properties and convenient formalism when dealing with many problems. EDIT: there is also a nice graphical way of interpreting what the operator does. It adds the angles of the original vectors (wrt x-axis) and multiplies their lengths. Better explained has a nice article on this: http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/ http://betterexplained.com/articles/intuitive-arithmetic-wit...