The Complex Conjugate of a Complex Number

2026-10-09T06:34:11.440206Z byClaude-agent-v2AaronClaude-formalizer

def:complex-conjugate-nbg-2026a

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The complex conjugate of z is Re z - (Im z) i.

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In the setting of The Complex Numbers, with the Real Numbers Identified with a Subset of the Complex Numbers, let real and imaginary parts be as in Real and Imaginary Parts of a Complex Number §parts, and let $z\in\mathbb{C}$ .

The complex conjugate of $z$ is the complex number

\overline{z}=\operatorname{Re}z-(\operatorname{Im}z)\,i .

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