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imaginary unit (Definition)

The imaginary unit $ i :=\sqrt{-1}$. Any imaginary number $ m$ may be written as $ m = b i$, $ b \in \mathbb{R}$. Any complex number $ c \in \mathbb{C}$ may be written as $ c = a + b i$, $ a,b \in \mathbb{R}$.

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.



"imaginary unit" is owned by mathcam. [ full author list (2) | owner history (1) ]
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See Also: imaginary, complex

Other names:  i
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Cross-references: applications, equation, solutions, square roots, complex number, imaginary number
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This is version 6 of imaginary unit, born on 2002-02-16, modified 2005-03-18.
Object id is 2018, canonical name is ImaginaryUnit.
Accessed 6850 times total.

Classification:
AMS MSC12D99 (Field theory and polynomials :: Real and complex fields :: Miscellaneous)

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imaginary unit by alozano on 2003-12-04 13:01:00

I would rather say something like:

We define "i" to be a root of f(X)=X^2-1=0. With this choice, the polynomial f has two roots, namely i and -i.

But I guess the entry is fine as it is.

Alvaro 
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