Definition:Argument of Complex Number/Mistake
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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:
- $3.7$ Complex Numbers and Functions: Polar Form
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