Imaginary unit (nonfiction): Difference between revisions
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[[File:Imaginary unit.svg|thumb|''i'' in the complex or cartesian plane. Real numbers lie on the horizontal axis, and imaginary numbers lie on the vertical axis.]]The '''imaginary unit''' or '''unit imaginary number''' (''i'') is a solution to the quadratic equation x2 + 1 = 0. There is no [[Real number (nonfiction)|real number]] with this property, hence the term imaginary. | [[File:Imaginary unit.svg|thumb|''i'' in the complex or cartesian plane. Real numbers lie on the horizontal axis, and imaginary numbers lie on the vertical axis.]]The '''imaginary unit''' or '''unit imaginary number''' (''i'') is a solution to the quadratic equation x2 + 1 = 0. There is no [[Real number (nonfiction)|real number]] with this property, hence the term imaginary. | ||
''i'' can be used to extend the real numbers | ''i'' can be used to extend the real numbers into [[Complex number (nonfiction)|complex numbers]], using addition and multiplication. A simple example of the use of ''i'' in a complex number is 2 + 3''i''. | ||
Imaginary numbers are an important mathematical concept, which extend the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every nonconstant polynomial P(x). | Imaginary numbers are an important mathematical concept, which extend the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every nonconstant polynomial ''P(x)''. | ||
There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every | There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every [[Real number (nonfiction)|real number]] other than zero, which has one double square root. | ||
In contexts where ''i'' is ambiguous or problematic, ''j'' or the Greek ι is sometimes used. In the disciplines of electrical engineering and control systems engineering, the imaginary unit is normally denoted by ''j'' instead of ''i'', because ''i'' is commonly used to denote electric current. | In contexts where ''i'' is ambiguous or problematic, ''j'' or the Greek ι is sometimes used. In the disciplines of electrical engineering and control systems engineering, the imaginary unit is normally denoted by ''j'' instead of ''i'', because ''i'' is commonly used to denote electric current. | ||
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== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Complex number (nonfiction)]] | |||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
* [[Real number (nonfiction)]] | |||
External links: | External links: | ||
Revision as of 19:12, 9 April 2018
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. There is no real number with this property, hence the term imaginary.
i can be used to extend the real numbers into complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.
Imaginary numbers are an important mathematical concept, which extend the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every nonconstant polynomial P(x).
There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
In contexts where i is ambiguous or problematic, j or the Greek ι is sometimes used. In the disciplines of electrical engineering and control systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current.
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Fiction cross-reference
Nonfiction cross-reference
External links:
- Imaginary unit @ Wikipedia