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Homework Help: Compute <z,w>

  1. Apr 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Compute <z,w> for z = [ (1+i)/2 , (1-i)/2 ], w = [ i/sqrt(2) , -1/sqrt(2) ]

    2. Equations

    <z , w> = z1 * w1 + 2 * z2 * w2

    where w1 and w2 have the conjugate sign over them.

    3. The attempt at a solution

    <z, w> = (1+i)/2 * (-i/sqrt(2)) + 2 * ((1-i)/2) (-1/sqrt(2))

    = -sqrt(2)/4 + sqrt(2)/4 * i

    Is the formula I used correct for this? Thanks!
  2. jcsd
  3. Apr 8, 2009 #2


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    Homework Helper

    Hi Squaremeplz

    I'm not sure what your formula is or why there is a 2 in it... did your formula come from somewhere, or are you supposed to use it for some reason?

    the usual complex inner product is defined as
    [tex] <u,v> = \sum u_i v_i* [/tex]
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