magnitude complex!!

$\dfrac{2z_1+7z_2}{2z_1-7z_2} = \\ \dfrac{2+7\frac{z_2}{z_1}}{2-7\frac{z_2}{z_1}}\\ \text{let }w = 2+ 7\frac{z_2}{z_1}\\ \dfrac{2+7\frac{z_2}{z_1}}{2-7\frac{z_2}{z_1}} = \dfrac{w}{w^*}$

$\text{You should know, or you can prove it as an exercise, that }\\ \forall z \in \mathbb{C},~z\neq 0,~\left|\dfrac{z}{z^*}\right| = 1 \text{ so,}\\ \left|\dfrac{2z_1+7z_2}{2z_1-7z_2}\right| = 1$