Complex conjugate ( $\overline{z}$ )

The complex conjugate of

z = x + i y

is

\overline{z} = x - i y

. It satisfies

z \overline{z} = ∣ z ∣^{2}

.

Table of contents
- Complex conjugation Complex conjugate

Complex conjugation ( $z \mapsto \overline{z}$ )

Complex conjugation sends a complex number

z = a + ib

to its complex conjugate

\overline{z} = a - ib

. It is an involution and a field automorphism of

C

, with fixed field

R

. Applied componentwise to a complex vector, it produces the conjugated vector appearing in a Choi state for a rank-one Kraus operator.

 Ancestors (6)

 Incoming links (72)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (2)

Complex conjugate by

Wikipedia Bot  1

The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. A complex number is typically expressed in the form: \[ z = a + bi \] where: - \( a \) is the real part, - \( b \) is the imaginary part, and - \( i \) is the imaginary unit with the property \( i^2 = -1 \).

 Read the full article

Complex conjugate by

Ciro Santilli  40 Updated 2025-07-16

 Read the full article

  See all articles in the same topic Create my own version