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complex_number [2014/01/29 19:06] nikolaj |
complex_number [2014/01/29 19:07] nikolaj |
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| @#FFBB00: $ \mathbb C \equiv \mathbb R^2 $ | | | @#FFBB00: $ \mathbb C \equiv \mathbb R^2 $ | | ||
==== Discussion ==== | ==== Discussion ==== | ||
- | We write the complex numbers as $a+ib\equiv\langle a,b\rangle$, where $a,b\in\mathbb R$. The complex numbers are then set up as a [[field]] with $i^2=-1$, see [[arithmetic structure of complex numbers]]. That structure of $\mathbb C$ is defined to extend the real numbers and these are identified as in $\mathbb C$ as $=\langle a,0\rangle=a+i0=a$. | + | We write the complex numbers as $a+ib\equiv\langle a,b\rangle$, where $a,b\in\mathbb R$. The complex numbers are then set up as a [[field]] with $i^2=-1$, see [[arithmetic structure of complex numbers]]. We identify the real numbers within $\mathbb C$ as the set of elements of the form $\langle a,0\rangle=a+i0=a$. |
=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Complex_number|Complex number]] | Wikipedia: [[http://en.wikipedia.org/wiki/Complex_number|Complex number]] |