Name of Inequality

Question

Let $x_i, y_i$ be complex numbers for all $i$.

Is there a name for the following inequality? $$\left| \sum_{i=1}^n x_i \right| \leq \sum_{j=1}^n |x_j| $$

In particular, is it a special case of this form of the Cauchy-Schwarz Inequality?

$$\left| \sum_{i=1}^n x_i \bar{y}_i \right|^2 \leq \sum_{j=1}^n |x_j|^2 \sum_{k=1}^n |y_k|^2 $$

Answer 1

Usually it's referred to as the triangle inequality.