imaginary unit

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

Note that there are two complex square roots of $-1$ (i.e. the two solutions to the equation $x^2+1=0$ in $ℂ$), 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
Canonical name	ImaginaryUnit
Date of creation	2013-03-22 12:21:14
Last modified on	2013-03-22 12:21:14
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	10
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 12D99
Synonym	i
Related topic	Imaginary
Related topic	Complex