Let $z_{1} \:and \:z_{2}$ be any two non-zero complex numbers such that $3|z_{1}| = 4|z_{2}|$. If $z= \frac{3z_{1}}{2z_{2}}+\frac{2z_{2}}{3z_{1}}$ then :

It is given that $z_{1} \:and \:z_{2}$  are two non- zero complex number such that,
$3|z_{1}| = 4|z_{2}|$
$z= \frac{3z_{1}}{2z_{2}}+\frac{2z_{2}}{3z_{1}}$
$= \frac{3}{2}(\frac{4}{3}.\frac{z_2}{z_2})+\frac{2.z_2}{3\times (4/3.z_2)}$
$\\=\frac{3}{2}\times \frac{4}{3}+\frac{1}{2}\\ =\frac{5}{2}$