This is how you do it:
Proposition: Let V be an inner-product space, and v, w in V. If v is orthogonal to w, then ||v+w||² = ||v||² + ||w||². More generally, if v1, v2...vn in V, and vi is orthogonal to vj wherever i is not equal to j, then
||(sum from 1 to n) vi ||² = (sum from 1 to...