View source for Logarithm of a quotient is a difference of logarithms

==Theorem==
Let $z_1, z_2 \in \mathbb{C} \setminus (-\infty,0]$ with $z_2 \neq 0$ and $- \pi < \mathrm{arg}(z_1) - \mathrm{arg}(z_2) \leq \pi$. Then the following formula holds:
$$\log \left( \dfrac{z_1}{z_2} \right) = \log(z_1) - \log(z_2),$$
where $\mathrm{arg}$ denotes the [[argument]] and $\log$ denotes the [[logarithm]].
==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued)|next=Relationship between logarithm (multivalued) and positive integer exponents}}: $4.1.9$

[[Category:Theorem]]
[[Category:Unproven]]