Is this function C → C injective?

Question

Consider f $\colon$ $\mathbb C $ $\to$ $\mathbb C$ given by f (z) = $z^3$

I know that this function is a surjection, but is it injective, thus bijective?

Answer 1

No, for example $f(1) = f(e^{2\pi i/3}) = f(e^{4\pi i/3}) = 1$.

[In fact, if you solve $f(z) = w$, you will get exactly three solutions for every $w\neq 0$.]