Question 9

Let $f(z) = (z + 2)^{\frac{1}{3}}(7 - z)^{\frac{2}{3}}$.

• If $f(z)$ is defined with branch cuts from $7$ to infinity along the positive real axis and from minus infinity to $-2$ along the negative real axis, and if $f(6) = 2$, find the limiting values of $f(z)$ as $z = -11$ is approached from above the real axis and from below the real axis.
• If instead $f(z)$ is defined with a branch cut the real interval $[-2, 7]$ and if $f(-11) = -9\sqrt[3]{4}$, find the limiting values of $f(z)$ as $z = 6$ is approached from above and from below the cut.