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complex_number [2014/01/29 19:06] nikolaj |
complex_number [2014/04/01 19:14] (current) nikolaj |
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| ===== Complex number ===== | ===== Complex number ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#FFBB00: $ \mathbb C \equiv \mathbb R^2 $ | | + | | @#FFBB00: definiendum | @#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]] | ||
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| === Subset of === | === Subset of === | ||
| [[Real coordinate space]] | [[Real coordinate space]] | ||
| - | === Element of === | ||
| - | [[Set]] | ||
