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Let \( z_{1} \) and \( z_{2} \) be any two non-zero complex numbers such that \( 3\left|z_{1}\right|=4\left|z_{2}\right| \). If \( z=\frac{3 z_{1}}{2 z_{2}}+\frac{2 z_{2}}{3 z_{1}} \), then
\( \mathrm{P} \)
(2019 Main, 10 Jan I)
W
(a) \( |z|=\frac{1}{2} \sqrt{\frac{17}{2}} \)
(b) \( \operatorname{Im}(z)=0 \)
(c) \( \operatorname{Re}(z)=0 \)
(d) \( |z|=\sqrt{\frac{5}{2}} \)
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