Show that the spin function
$$
x=2^{1 / 2}\binom{1}{i e^{i \varphi}}
$$
represents a spin pointing in the direction of the normal
$$
\hat{\mathbf{n}}=\frac{\mathbf{k}_{\mathrm{i}} \times \mathbf{k}_{\mathrm{f}}}{\left|\mathbf{k}_{\mathrm{i}} \times \mathbf{k}_{\mathrm{f}}\right|}
$$
The polar coordinate system is chosen such that $\mathbf{k}_i$ is the polar axis, and $k_f$ has the angular coordinates $\theta, \varphi$.