## Mathematical methods Q - Find Domain where analytic

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).