Definition:Complex Number/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 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

 * Definition:Imaginary Part