Isomorphisms of the ring of truncated polynomials over the complex numbers

Question

I have to prove that the factor ring $\mathbb{C}[[z]]/z^m\mathbb{C}[[z]]$ is isomorphic to the ring of truncated polynomials $\mathbb{C}[z]/(z^m)$, where $\mathbb{C}[[z]]$ is the ring of formal power series over the complex numbers, but I can't come up with any specific ring isomorphism to prove it with. I know that every ideal in $\mathbb{C}[[z]]$ is of the form $(z^m)$ for some $m$, but i can't see how that will help, unless there is some way of identifying $(z^m)$ and $z^m\mathbb{C}[[z]]$.