# Differences

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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 Both sides previous revision Previous revision 2013/08/07 13:04 nikolaj 2013/08/06 21:23 nikolaj 2013/08/06 21:13 nikolaj created 2013/08/07 13:04 nikolaj 2013/08/06 21:23 nikolaj 2013/08/06 21:13 nikolaj created Line 1: Line 1: ===== 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]]