Let z_1 and z_2 be any two non-zero complex n | vedclass

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Question

$\left|\frac{3 z_{1}}{2 z_{2}}ight|=2$

Let $\frac{3 z_{1}}{2 z_{2}}=2 \cos 	heta+2(\sin 	heta) i$

$\Rightarrow \frac{2 z_{2}}{3 z_{1}}=\frac

Vedclass · Accepted Answer

Im$(z) 
eq 0$

Vedclass · Answer

$\left|\frac{3 z_{1}}{2 z_{2}}ight|=2$

Let $\frac{3 z_{1}}{2 z_{2}}=2 \cos 	heta+2(\sin 	heta) i$

$\Rightarrow \frac{2 z_{2}}{3 z_{1}}=\frac{1}{2} \cos 	heta-\frac{1}{2}(\sin 	heta)$

Given, $z=\frac{2 z_{1}}{3 z_{2}}+\frac{3 z_{2}}{2 z_{1}}$ $=\frac{5}{2} \cos 	heta+\frac{3}{2}(\sin 	heta) i$

Which is neither purely real nor purely imaginary and $|z|$ depends on $	heta$.

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

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