For the vectors $u = (a,b), v = (c,d)$ in $C^{2}$ the inner product of $u$ and $v$ is defined by $\langle u,v \rangle = a\bar{c} + b\bar{d}$. If $u = (1+i, i), v = (i, 1-i)$ then $\langle u,v \rangle = $
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Don't forget the bar ($\bar{c}$)! In complex spaces, the second vector's components must be conjugated.