# inverse number

The inverse number or reciprocal number of a non-zero real or complex number $a$ may be denoted by $a^{-1}$, and it the quotient $\frac{1}{a}$ (so, it is really the $-1^{\mathrm{th}}$ power of $a$).

• Two numbers are inverse numbers of each other if and only if their product is equal to 1 (cf. opposite inverses).

• If $a$ ($\neq 0$) is given in a quotient form $\frac{b}{c}$, then its inverse number is simply

 $\left(\frac{b}{c}\right)^{-1}=\frac{c}{b}.$
• Forming the inverse number is also a multiplicative function, i.e.

 $(bc)^{-1}=b^{-1}c^{-1}$

(to be more precise, it is an automorphism of the multiplicative group of $\mathbb{R}$ resp. $\mathbb{C}$).

 Title inverse number Canonical name InverseNumber Date of creation 2013-03-22 14:53:46 Last modified on 2013-03-22 14:53:46 Owner pahio (2872) Last modified by pahio (2872) Numerical id 12 Author pahio (2872) Entry type Definition Classification msc 12E99 Classification msc 00A05 Synonym inverse Synonym reciprocal Related topic ConditionOfOrthogonality Related topic InverseFormingInProportionToGroupOperation Defines reciprocal number