We have four multivalued functions: $f\left( z\right) =\left( \dfrac {z-1}{z+1}\right) ^{\dfrac {1}{2}}$ $g\left( z\right) =\left( \dfrac {z-1}{z+1}\right) ^{\dfrac {1}{3}}$ $h\left( z\right) =\left( z^{2}-1\right) ^{\dfrac {1}{2}}$ $k\left( z\right) =\left( z^{2}-1\right) ^{\dfrac {1}{3}}$
a) Show that one can define branches to all four functions in $\Omega =C\backslash [-1,+\infty [$
b) Show that branches exist for f, g and h but not for k in $\Omega =C\backslash [-1,1 ]$