Definition:Complex Number/Imaginary Part

Definition

The imaginary part of a complex number $a + i b$ is the coefficient $b$ (note: not $i b$).

The imaginary part of a complex number $z$ is often denoted $\Im \left({z}\right)$ or $\operatorname{Im} \left({z}\right)$ or $\operatorname{im} \left({z}\right)$.

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:

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

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

$\operatorname{im} \left({z}\right)$

or a similar variant.

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 12$: Example $12.3$
• Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (1968): $\S 1.2.2$