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--- complex_number [2014/01/29 19:02]
nikolaj
+++ complex_number [2014/01/29 19:07]
nikolaj
@@ Line 3: / Line 3: @@
 | @#FFBB00: $ \mathbb C \equiv \mathbb R^2 $ |
 ==== Discussion ====
-We write the complex numbers as $a+ib\equiv\langle a,b\rangle$. We can more formally set up the complex numbers as a [[field]] with $i^2=-1$, see [[arithmetic structure of complex numbers]]. They are defined to extend the real numbers $\mathbb R$, identified within $\mathbb C$ 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 ===
 Wikipedia: [[http://en.wikipedia.org/wiki/Complex_number|Complex number]]