The function is $f(z) = \frac{\sin{z}}{z^3 + 1}$. My tactic was
- Express f(z) in cartesian form.
- Find $\frac{\partial u}{\partial x}$, $\frac{\partial u}{\partial y}$. $\frac{\partial v}{\partial x}$, $\frac{\partial v}{\partial y}$.
- Compute the set $\{x + iy : (\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}) \land (\frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x})\}$
However, this quickly became algebraically unwieldly. Is my way even correct? Is there a better way to solve this problem?