Branch Cut question for a complex logarithm function (i think i understand it)

Hi there.

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) = -i*π. 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 -3*π*/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(5*π/6 +2k**π)*

since it must lie on the branch i chose...

ln2 + i(5*π/6 - 2**π)*

= ln2 - 7*πi/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.