Definition:Complex Number/Imaginary Part

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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 $\mathsf{Pr} \infty \mathsf{fWiki}$ by $\Im \paren z$.


Also denoted as

Variants of $\operatorname{Im} \left({z}\right)$ that can often be found are:

$\operatorname {Im} \paren z$
$\operatorname {\mathscr I} \paren z$
$\operatorname {im} \paren z$
$\operatorname {\mathfrak I} \paren z$


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


Sources