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complex_conjugate_of_a_complex_number [2013/08/06 21:23] nikolaj |
complex_conjugate_of_a_complex_number [2013/08/07 13:04] nikolaj |
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| ===== Complex conjugate of a complex number ===== | ===== Complex conjugate of a complex number ===== | ||
| ==== Definition ==== | ==== Definition ==== | ||
| - | | @#88DDEE: $z\equiv a+i\ b\in \mathbb C$ | @#88DDEE: $a,b\in\mathbb R$ | | + | | @#88DDEE: $X\subseteq\mathbb C$ |
| - | | @#55EE55: $\overline z\equiv a-i\ b$ | | + | | @#55EE55: $\mathrm{conj}:X\to \mathbb C$ | |
| + | | $a+i\ b\in X$ | $a,b\in \mathbb R$ | | ||
| + | |||
| + | | @#55EE55: $\mathrm{conj}(a+i\ b):= a-i\ b$ | | ||
| ==== Ramifications ==== | ==== Ramifications ==== | ||
| + | If $z\in \mathbb C$, one writes $\overline z\equiv\mathrm{conj}(z)$. | ||
| ==== Context ==== | ==== Context ==== | ||
| === Parents === | === Parents === | ||
| [[Complex number]] | [[Complex number]] | ||
