Triangle inequality

|V_i + V_j|²  = |V_i|² + |V_j|² + <V_i|V_j> + <V_j|V_i>
= |V_i|² + |V_j|² + 2 Re(<V_i|V_j>)
≤ |V_i|² + |V_j|² + 2 Re(|V_i||V_j|) = |V_i|² + |V_j|² + 2|V_i||V_j| = (|V_i| + |V_j|)².
Therefore  |V_i + V_j| ≤ |V_i| +|V_j|.