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 :

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 :

${\rm I}m\left( z \right) = 0$

$\left| z \right| = \sqrt {{17 \over 2}} $

$\left| z \right| =$ ${1 \over 2}\sqrt {9 + 16{{\cos }^2}\theta } $

Re(z) $=$ 0

Solution

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