Chapter 5 - Inner Product Spaces - 5.1 Definition of an Inner Product Space - Problems - Page 350: 7

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We are given: $v=(6-3i,4,-2+5i,3i) \\ w=(i,2i,3i,4i)$ Since, we have $(v,w)=(6-3i)(-i)+4(-2i)+(-2+5i)(-3i)+3i(-4i)=24-8i\\$ $||v||=\sqrt (v,v)=\sqrt (6-3i)(6+3i)+4.4+(-2+5i)(-2-5i)+3i(-3i)=\sqrt 99$ $||w||=\sqrt (w,w)=\sqrt i(-i)+2i)(-2i)+3i(-3i)+4i(-4i)=\sqrt 30$