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imaginary unit
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(Definition)
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The imaginary unit $i \defined \sqrt{-1}$ Any imaginary number $m$ may be written as $m = b i$ $b \in \reals$ Any complex number $c \in \complexes$ may be written as $c = a + b i$ $a,b \in \reals$
Note that there are two complex square roots of $-1$ (i.e. the two solutions to the equation $x^2+1=0$ in $\mathbb{C}$ , so there is always some ambiguity in which of these we choose to call ``$i$ ' and which we call ``$-i$ ', though this has little bearing on any applications of complex numbers.
In physics and some engineering fields, the symbol $j$ is used for the imaginary unit.
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"imaginary unit" is owned by Mathprof. [ full author list (3) | owner history (2) ]
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Cross-references: fields, applications, equation, solutions, square roots, complex, complex number, imaginary number
There are 12 references to this entry.
This is version 7 of imaginary unit, born on 2002-02-16, modified 2008-12-24.
Object id is 2018, canonical name is ImaginaryUnit.
Accessed 8442 times total.
Classification:
| AMS MSC: | 12D99 (Field theory and polynomials :: Real and complex fields :: Miscellaneous) |
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Pending Errata and Addenda
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