TITLE: What is the symbol for imaginary numbers?
QUESTION [16 upvotes]: $\mathbb Q$ is used to represent rational numbers. $\mathbb R$ is used to represent real numbers. Is there an accepted symbol for imaginary numbers?

REPLY [9 votes]: There is an accepted symbol for complex numbers, $\textbf{C}$. The others seem to have assumed you already know this symbol, but from your question it is not entirely clear if you do or do not.
If you are referring to purely imaginary numbers, numbers $z$ such that $\Re(z) = 0$, then the answer is no, there is no accepted symbol for imaginary numbers.
The consensus here is that if you really need a symbol, you could go with $\textbf{I}$ but would be much better off with $i \textbf{R}$.
And yeah, it is easy to conclude that the purely imaginary numbers are "boring." After all, they are closed under addition but not multiplication, whereas purely real numbers are. This is also true of real rational numbers.
But we should also consider the context in which you need a symbol for purely imaginary numbers. Do you mean to say that a particular number $bi$ is purely imaginary? You could write $bi \in i \textbf{R}$. But then it would be just much easier to write $b \in \textbf{R}$, and then it is clear that $\Re(bi) = 0$.
It seems a little strange that $0$ is both purely real and purely imaginary. If you need to say that $bi$ is a nonzero purely real imaginary number, you could write that $\Re(bi) = 0$ but $\Im(bi) \neq 0$.