# Definition:Complex Number/Real Part

(Redirected from Definition:Real Part)

## Definition

Let $z = a + i b$ be a complex number.

The real part of $z$ is the coefficient $a$.

The real part of a complex number $z$ is usually denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ by $\map \Re z$ or $\Re z$.

## Also denoted as

Variants of $\Re \paren z$ that can often be found are:

$\map {\mathrm {Re} } z$
$\map {\mathscr R} z$
$\map {\mathrm {re} } z$
$\map {\mathfrak R} z$
$\map {\mathbf R} z$ or $\mathbf R z$

While the fraktur font is falling out of fashion, because of its cumbersome appearance and difficulty to render in longhand, its use for this application is conveniently unambiguous.

## Also see

• Results about real parts can be found here.