Unformatted text preview: z = x + i y we deﬁned ¯ z := xi y and  z  = √ ¯ zz . Show that (i) ( a ) z 1 + z 2 = ¯ z 1 + ¯ z 2 ( b ) z 1 z 2 = ¯ z 1 ¯ z 2 ( c ) z 1 /z 2 = ¯ z 1 / ¯ z 2 ( d ) ¯ ¯ z = z (ii) ( e )  z 1 z 2  =  z 1  z 2  ( f )  z 1 + z 2  ≤  z 1  +  z 2  6. (i) Find x,y ∈ R such that ( a ) e i π 3 = x + i y ( b ) 2e i π 2 = x + i y ( c ) 10e i 7 π 6 = x + i y and compare with Question 2 . (ii) Find r ∈ R + , ϕ ∈ [0 , 2 π ) such that ( a ) 1 + i = r e i ϕ ( b )5i = r e i ϕ ( b )3 + 4i = r e i ϕ and compare with Question 1 . 1...
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 Spring '10
 Spyros
 Linear Algebra, Algebra, Vectors, Vector Space, Complex number, Vector Motors, π π, arbitrary vectors

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