Question

Find the principal value of loge(-3)​

Answer 1

Answer:

Let’s start with log(−1) , since that one we know: log(−1)=πi(+2kπ) for any k∈Z.

Also, we know that log(ab)=log(a)+log(b)

So, we get that log(−3)=log(3)+πi+(2kπ),k∈Z. Here log(3) will just be the ordinary (real) logarithm of 3. The principal value is log(3)+πi.