Definition:Complex Number/Real Part

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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 $\Re \paren z$.

Also denoted as

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

$\operatorname {Re} \paren z$
$\operatorname {\mathscr R} \paren z$
$\operatorname {re} \paren z$
$\operatorname {\mathfrak R} \paren z$

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