Chapter 3.10, Problem 10P

Prove that This is called the triangle inequality; in two or three dimensions, it simply says that the length of one side of a triangle $\le$ sum of the lengths of the other 2 sides. Hint: To prove it in n-dimensional space, write the square of the desired inequality using $\left(10.2\right)$ and also use the Schwarz inequality $\left(10.4\right).$ Generalize the theorem to complex Euclidean space by using $\left(10.7\right)$ and $\left(10.9\right).$