Definition:Argument of Complex Number/Mistake

Source Work

 * $3$: Elementary Analytic Methods
 * $3.7$ Complex Numbers and Functions: Polar Form
 * $3.7.4$: Argument:

Mistake

 * $\arg z = \map \arctan {y / x} = \theta$

Correction
Should read something like:

$\arg z$ is formally defined as a solution to the pair of equations:
 * $(1): \quad \dfrac x {\cmod z} = \map \cos {\arg z}$
 * $(2): \quad \dfrac y {\cmod z} = \map \sin {\arg z}$

where $\cmod z$ is the modulus of $z$.

See Warning: Flawed Definition.