Prove that |v+u| is less than or equal to |v| + |u| wher v and u are complex numbers.

My attempt:

I though I would substitute v = a + bi and u = x + yi to the equation |v+u| > |v| + |u| and try to find a contradiction.

I got to 2abxy > (ay)^2 + (bx)^2 but this doesn't seem to be obviously false. Is my approach correct or is there a better way to prove this?