Definition:Argument of Complex Number/Mistake

Source Work

1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions

$3$: 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.

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: $3.7.4$: Argument