Unformatted text preview: z 1 6 = 0 then 1 /z 1 ∈ Q ( √ 2) (hint: use the fact that √ 2 is irrational.) (iv) If z 1 6 = 0 then z 2 /z 1 ∈ Q ( √ 2) 3. Compute the following dot products and determine the cosine of the angle between the vectors. ( a ) ± 1 2 ² · ± 68 ² ( b ) ±73 ² · ± 1 ² 4. Use the relation between the norm and the dotproduct, k v k 2 = v · v , to show (i) the parellelogram law: k vw k 2 + k v + w k 2 = 2 k v k 2 + 2 k w k 2 (ii) the polarisation identity: v · w = 1 4 ( k v + w k 2 k vw k 2 ) 1...
View
Full Document
 Spring '10
 Spyros
 Linear Algebra, Algebra, Geometry, Vector Space, Complex number, following relations cos

Click to edit the document details