Branch Cut question for a complex logarithm function (i think i understand it)
I'm new to this whole branch cut concept and was working on the following question. I want to be sure my logic is correct.
The question was...
consider a branch of logz corresponding to the branch cut x = 0, y >= 0 and value log(-1) = -iπ. I must calculate log(-(3^1/2) + i) relative to this branch.
From the little information I have gathered about branch cuts, i have deduced (possibly incorrectly) that The "branch cut" x = 0, y >= 0 starts the branch at -3π/2 and ends it at π/2 because it must contain a z with it's argument equal to -π
I then went along to get the general log(-(3^1/2) + i) and found it to be...
ln2 + i(5π/6 +2kπ)
since it must lie on the branch i chose...
ln2 + i(5π/6 - 2π)
= ln2 - 7πi/6
Am I getting this? I'm sorry but I came late to this lecture and had to sit in the back where i couldn't see half the board because of the guy with the fat head in front of me.