**Taking logarithms of Complex Numbers**
Recall the we could express any complex number,

by the following:

where

and

With all the background knowledge I gave, I don't think it is hard for the average reader to see where I'm going with this, so I'll just say it.

We can take the logarithm of a complex number by making use of the following formula:

or equivalently (by applying Law 5):

or to simplify even more (by applying Law 1):

[snipped]

**Questions:**

- Was everything I said correct? Would anyone like to add anything that can deepen my, as well as other readers', understanding?