Definition:Complex Number/Imaginary Part

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

The imaginary part of $z$ is the coefficient $b$ (note: not $i b$).

The imaginary part of a complex number $z$ is usually denoted on by $\map \Im z$ or $\Im z$.

Also denoted as
Variants of $\map \Im z$ that can often be found are:


 * $\map {\mathrm {Im} } z$
 * $\map {\mathscr I} z$
 * $\map {\mathrm {im} } z$
 * $\map {\mathfrak I} z$

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:Real Part