# imaginary unit

The imaginary unit $i:=\sqrt{-1}$. Any imaginary number $m$ may be written as $m=bi$, $b\in\mathbb{R}$. Any complex number $c\in\mathbb{C}$ may be written as $c=a+bi$, $a,b\in\mathbb{R}$.

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.

Title imaginary unit ImaginaryUnit 2013-03-22 12:21:14 2013-03-22 12:21:14 Mathprof (13753) Mathprof (13753) 10 Mathprof (13753) Definition msc 12D99 i Imaginary Complex