The imaginary unit $i \defined \sqrt{-1}$ Any imaginary number $m$ may be written as $m = b i$ $b \in \reals$ Any complex number $c \in \complexes$ may be written as $c = a + b i$ $a,b \in \reals$

Note that there are two complex square roots of $-1$ (i.e. the two solutions to the equation $x^2+1=0$ in $\mathbb{C}$ , so there is always some ambiguity in which of these we choose to call ``$i$ ' and which we call ``$-i$ ', though this has little bearing on any applications of complex numbers.

In physics and some engineering fields, the symbol $j$ is used for the imaginary unit.