What is the difference in notation for Ln(z) vs. ln(z) We are learning about the principal vs. non-principal values of the natural logarithm. There are 2 problems:


*

*$\ln(-7)$

*$\operatorname{Ln}(-7)$
I solved $\ln(-7)$ for:
$$=\ln|-7|+i\pi+2\pi k$$
Is the difference in notation for the other problem really just removing the $2\pi k$? Or maybe it would be better if I define the argument like $-\pi<\theta<\pi$?

It is a convention in complex analysis to denote the principle branch of a multivalued function by capitalizing the first letter.
In this case, $\operatorname{Ln}(z) = \operatorname{Ln}|z|+i \operatorname{Arg}(z)$
As for $\operatorname{Ln}$, $\operatorname{Arg}$ is the principle branch of the the argument function, taking values in $(-\pi, \pi]$.
