Chapter 5 - Inner Product Spaces - 5.1 Definition of an Inner Product Space - Problems - Page 350: 6

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We are given: $v=(2+i,3-2i,4+i,4+i) \\ w=(-1+i,1-3i,3-i)$ Since, we have $(v,w)=(2+i)(-1-i)+(3-2i)(1+3i)+(4+i)(3+i)=19+11i\\$ $||v||=\sqrt (v,v)=\sqrt (2+i)(2-i)+(3-2i)(3+2i)+(4+i)(4-i)=\sqrt 35$ $||w||=\sqrt (w,w)=\sqrt (-1+i)(-1-i)+(1-3i)(1+3i)+(3-i)(3+i)=\sqrt 22$