# Compute <z,w>

1. Apr 8, 2009

### squaremeplz

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. Apr 8, 2009

### lanedance

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
$$<u,v> = \sum u_i v_i*$$