Let z₁ and z₂ be any two non-zero complex numbers such that 3|z₁| = 4 |z₂|.
If z = 3z₁/2z₂ + 2z₂/3z₁ then :
(1) Re (z) = 0
(2) |z| = √5/2
(3) |z| = 1/2√17/2
(4) |m(z) = 0