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In mathematics, an '''imaginary number''' is a [[complex number]] that is not [[real number|real]]. The term is not generally used because complex numbers (e.g., <math>3 + 4i</math>) have two components, a [[real part]] (in this  case 3), and an [[imaginary part]] (in this case 4). A complex number is said to be ''real'' if the imaginary part is 0, and in all other cases it is non-real. In most cases, when people speak of imaginary numbers, they are not referring to complex numbers which are not real, but complex numbers with the real part of 0. For clarity, such numbers are usually called ''pure imaginary''.
The '''imaginary numbers''' are a part of the [[complex number]]s.
Every complex number can be written as
the sum ''a''+''b''i of a real number ''a'' and an imaginary number ''b''i
(with real numbers ''a'' and ''b'', and the '''imaginary unit''' i).
In the [[complex plane]] the imaginary numbers lie on the imaginary axes.
perpendicular to the real axes,
 
However, sometimes the term "imaginary" is used more generally
for all non-real complex numbers,
i.e., all numbers with non-vanishing imaginary part (''b'' not 0),
are called "imaginary".
In this case, the more specific complex numbers ''b''i
(with vanishing real part ''a''=0) are called '''pure(ly) imaginary'''.
 
 


The terms ''real'' and ''imaginary'' are misnomers; they should not be taken literally.
The terms ''real'' and ''imaginary'' are misnomers; they should not be taken literally.


For more information, see '''[[Complex number]]'''.
For more information, see '''[[Complex number]]'''.

Revision as of 20:21, 31 December 2009

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The imaginary numbers are a part of the complex numbers. Every complex number can be written as the sum a+bi of a real number a and an imaginary number bi (with real numbers a and b, and the imaginary unit i). In the complex plane the imaginary numbers lie on the imaginary axes. perpendicular to the real axes,

However, sometimes the term "imaginary" is used more generally for all non-real complex numbers, i.e., all numbers with non-vanishing imaginary part (b not 0), are called "imaginary". In this case, the more specific complex numbers bi (with vanishing real part a=0) are called pure(ly) imaginary.


The terms real and imaginary are misnomers; they should not be taken literally.

For more information, see Complex number.

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