Example:

For $N=3$ we have, in general,

$$\left<\underline{u},\underline{v}\right> = u_0 \overline{v_0} + u_1 \overline{v_1} + u_2 \overline{v_2}.$$

Let

$$\begin{eqnarray*} \underline{u}&=& [0,j,1] \\ \underline{v}&=& [1,j,j]. \end{eqnarray*}$$

Then

$$\left<\underline{u},\underline{v}\right> = 0\cdot 1 + j \cdot (-j) + 1 \cdot (-j) = 0 + 1 + (-j) = 1-j.$$

See §I.3.1 regarding computation of inner products in the matlab programming language.