ThmDex – An index of mathematical definitions, results, and conjectures.

Complex conjugation is a multiplicative operation

Formulation 0

Let $z_1, \dots, z_N \in \mathbb{C}$ each be a D1207: Complex number.

Then \begin{equation} \overline{\prod_{n = 1}^N z_n} = \prod_{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}

Also known as

Complex conjugate of finite complex product equals product of complex conjugates, Multiplicativity of complex conjugation, Complex conjugation preserves finite complex products

Subresults

▶	R5297: Complex conjugate of a product of two complex numbers