Hi, im really stuck on this question. Thankyou for any help in advance :)

5)

i) Find a domain on which the function

g1(z) = ln[(z − 4)/(z^2 − 4)]

is single valued and analytic.

Provide two alternative constructions:

a) Take the

principal branch cut for ln (z) and

b) take the branch cut for ln (z) to be R+.

ii) Find a domain on which the function

g2(z) = arcsinh z

is single valued and analytic. Use the principal branch cut for ln (z).