MultiplicationPlanetmathPlanetmath is a mathematical operationMathworldPlanetmath in which two or more numbers are added up to themselves by a factor of other numbers. For example, 2×3=2+2+2=3+3=6. The numbers may be real, imaginaryPlanetmathPlanetmath or complex, they may be integers or fractions. Among real numbers, if an odd numberMathworldPlanetmathPlanetmath of multiplicands are negative, the overall result is negative; if an even number of multiplicands are negative, the overall result is positive. Two examples: (-3)×(-5)=15; (-2)×(-3)×(-5)=(-30).

The usual operator is the cross with its four arms of equal length pointing northeast, northwest, southeast and southwest: ×. Other options are the central dot and the tacit multiplication operator. In many computer programming languages the asterisk is often used as it is almost always available on the keyboard (Shift-8 in most American layouts, as well as dedicated key if the keyboard has a numeric keypad), and this is the operator likely to be used in a computer implementation of a reverse Polish notationMathworldPlanetmath calculator. In Mathematica, the space can sometimes function as a multiplication operator, but more experienced users warn novices not to rely on this feature.

Just as with addition, multiplication is commutative: xyz=xzy=yxz, etc.

The iterative operator is the Greek capital letter pi:


which is a compactPlanetmathPlanetmath way of writing a1×a2××an.

Multiplication of complex numbersMathworldPlanetmathPlanetmath is helped by the following identity: (a+bi)×(x+yi)=(ax-by)+(ay+bx)i. To give three examples: (17+29i)(11+38i)=-915+965i (the result has both real and imaginary parts), (1+2i)(1-2i)=5 (the result is a real prime) and (4+7i)(7+4i)=65i (the result has only an imaginary part).

Title multiplication
Canonical name Multiplication
Date of creation 2013-03-22 16:35:37
Last modified on 2013-03-22 16:35:37
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 10
Author PrimeFan (13766)
Entry type Definition
Classification msc 00A06
Classification msc 11B25
Classification msc 00A05
Related topic Product
Related topic ProductOfNegativeNumbers
Related topic FactorsWithMinusSign