For the scaling numbers

\[\begin{aligned}& \alpha_{1}=\frac{1+\sqrt{3}}{4 \sqrt{2}} \\& \alpha_{2}=\frac{3+\sqrt{3}}{4 \sqrt{2}} \\& \alpha_{3}=\frac{3-\sqrt{3}}{4 \sqrt{2}} \\& \alpha_{4}=\frac{1-\sqrt{3}}{4\sqrt{2}}\end{aligned}\]

verify the following identity:

(a) \(\alpha_{1}^{2}+\alpha_{2}^{2}+\alpha_{3}^{2}+\alpha_{4}^{2}=1\)

(b) \(\alpha_{1}+\alpha_{2}+\alpha_{3}+\alpha_{4}=\sqrt{2}\)