I've just started learning about the quaternions and it's raised some interesting questions for me about the complex numbers.
The $+$ sign in the expression $a+bi$ is confusing me. Usually when we use the $+$ sign it represents an operation combining two elements of the same space; $3+2=5$, $+$ is the operation of combining these two integers into a new integer. With the complex numbers the + sign in for example $1+i$ doesn't represent an operation. How could you combine an (strictly) imaginary number and a real number?
Apologies for the poorly expressed question, but any help would be greatly appreciated.