# Let V=C³ with the standard inner product. Let x=(2,1+i,i) and y=(2-i,2,1+2i). Compute <x,y>,||x||,||y|| and ||x+y||². Then verify both Cauchy's inequality and the triangle inequality.

Question

Let V=C³ with the standard inner product. Let x=(2,1+i,i) and y=(2-i,2,1+2i). Compute <x,y>,||x||,||y|| and ||x+y||². Then verify both Cauchy's inequality and the triangle inequality.