ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5298 on D507: Complex conjugate
Complex conjugatation is an additive operation
Formulation 0
Let $z_1, \dots, z_N \in \mathbb{C}$ each be a D1207: Complex number.
Then \begin{equation} \overline{\sum_{n = 1}^N z_n} = \sum_{n = 1}^N \overline{z_n} \end{equation}
Formulation 1
Let $z_1, \dots, z_N \in \mathbb{C}$ each be a D1207: Complex number.
Then \begin{equation} \overline{z_1 + z_2 + \cdots + z_N} = \overline{z}_1 + \overline{z}_2 + \cdots + \overline{z}_N \end{equation}