# 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

^{}$c\in \u2102$ 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 $\u2102$), 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 |