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 $\operatorname{Im} \left({z}\right)$.

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


 * $\Im \left({z}\right)$
 * $\operatorname {\mathscr I} \left({z}\right)$
 * $\operatorname {im} \left({z}\right)$
 * $\operatorname {\mathfrak{Im} } \left({z}\right)$