JEE Math Practice Question

Let z1 and z2 be any two non-zero complex numbers such that $$3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|.$$ If $$z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}}$$ then :

1. A.$${\rm I}m\left( z \right) = 0$$
2. B.$$\left| z \right| = \sqrt {{17 \over 2}} $$
3. C.$$\left| z \right| =$$ $${1 \over 2}\sqrt {9 + 16{{\cos }^2}\theta } $$
4. D.Re(z) $$=$$ 0