Definition:Imaginary Part/Polar Form

Definition

Let $z$ be a complex number expressed in polar form:

$z = \polar {r, \theta}$

The imaginary part of $z$ is:

$\map \Im z = r \sin \theta$

Also see

• Definition:Real Part

• Results about imaginary parts can be found here.

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.7$ Complex Numbers and Functions: Polar Form: $3.7.6$: Imaginary Part