Question: Find the number of solutions of the equation: $$z^3 + \frac{3(\bar z)^2}{|z|} = 0$$
I substituted $z = re^{i\theta}$ to convert the equation into: $$r^3e^{i3\theta} + 3re^{i2\theta}=0$$
This can be rearranged to be written as: $$re^{i2\theta}[r^2e^{i\theta} + 3] = 0$$
The only two solutions I see for this equation are $\theta = \pi$ and $r = \pm\sqrt3$. However, the answer given is 5. What have I dont wrong?
