The set \begin{equation*} T=\set{\vect{u}_1,\,\vect{u}_2,\,\vect{u}_3} =\set{ \colvector{1\\1+i\\1},\, \frac{1}{4}\colvector{-2-3i\\1-i\\2+5i},\, \frac{1}{11}\colvector{-3-i\\1+3i\\-1-i} } \end{equation*} from Example GSTV is an orthogonal set.
We compute the norm of each vector, \begin{align*} \norm{\vect{u}_1}=2&& \norm{\vect{u}_2}=\frac{1}{2}\sqrt{11}&& \norm{\vect{u}_3}=\frac{\sqrt{2}}{\sqrt{11}} \end{align*}
Converting each vector to a norm of 1, yields an orthonormal set, \begin{align*} \vect{w}_1&=\frac{1}{2}\colvector{1\\1+i\\1}\\ \vect{w}_2&=\frac{1}{\frac{1}{2}\sqrt{11}}\frac{1}{4}\colvector{-2-3i\\1-i\\2+5i}=\frac{1}{2\sqrt{11}}\colvector{-2-3i\\1-i\\2+5i}\\ \vect{w}_3&=\frac{1}{\frac{\sqrt{2}}{\sqrt{11}}}\frac{1}{11}\colvector{-3-i\\1+3i\\-1-i}=\frac{1}{\sqrt{22}}\colvector{-3-i\\1+3i\\-1-i} \end{align*}