Triangle Inequality/Complex Numbers/General Result

Theorem
Let $z_1, z_2, \ldots, z_m \in \C$ be complex numbers.

Let $\left\vert{z}\right\vert$ be the modulus of $z$.

Then:
 * $\left\vert{z_1 + z_2 + \cdots + z_m}\right\vert \le \left\vert{z_1}\right\vert + \left\vert{z_2}\right\vert + \cdots + \left\vert{z_m}\right\vert$