Difference between revisions of "Imaginary number"
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:<math>\sqrt{-1}= \pm i</math>. | :<math>\sqrt{-1}= \pm i</math>. | ||
| − | When a imaginary number is added to real number, they form a [[complex number]]. | + | When a imaginary number is added to real number, they form a [[complex number]]. Imaginary numbers are mathematically useful because they ensure that every polynomial [[equation]] has a solution - for example, the equation <math>x^2+1=0</math> has no real solution. |
The analysis of imaginary numbers forms the basis for the field of [[mathematics]] known as | The analysis of imaginary numbers forms the basis for the field of [[mathematics]] known as | ||
Revision as of 20:56, November 14, 2008
An imaginary number in mathematics is any number that contains the imaginary unit, defined as, <math>i^{2} = -1</math>
An imaginary number is of the form, <math>k i</math>, where k is a real number.
For example <math>\sqrt{-1}</math> has imaginary representation of
- <math>\sqrt{-1}= \pm i</math>.
When a imaginary number is added to real number, they form a complex number. Imaginary numbers are mathematically useful because they ensure that every polynomial equation has a solution - for example, the equation <math>x^2+1=0</math> has no real solution.
The analysis of imaginary numbers forms the basis for the field of mathematics known as complex analysis.