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

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(D) Given $3|z_1| = 4|z_2|$,we have $\left|\frac{3z_1}{2z_2}\right| = \frac{3|z_1|}{2|z_2|} = \frac{4|z_2|}{2|z_2|} = 2$.Let $w = \frac{3z_1}{2z_2}$.

Vedclass · Accepted Answer

$	ext{Im}(z) 
eq 0$

Vedclass · Answer

(D) Given $3|z_1| = 4|z_2|$,we have $\left|\frac{3z_1}{2z_2}ight| = \frac{3|z_1|}{2|z_2|} = \frac{4|z_2|}{2|z_2|} = 2$.Let $w = \frac{3z_1}{2z_2}$. Then $|w| = 2$,so we can write $w = 2(\cos 	heta + i \sin 	heta)$.Then $z = w + \frac{1}{w} = 2(\cos 	heta + i \sin 	heta) + \frac{1}{2(\cos 	heta + i \sin 	heta)}$.$z = 2(\cos 	heta + i \sin 	heta) + \frac{1}{2}(\cos 	heta - i \sin 	heta)$.$z = (2 + \frac{1}{2}) \cos 	heta + i(2 - \frac{1}{2}) \sin 	heta = \frac{5}{2} \cos 	heta + i \frac{3}{2} \sin 	heta$.Since $	ext{Im}(z) = \frac{3}{2} \sin 	heta$,it is not necessarily zero for all $	heta$. Thus,$	ext{Im}(z) 
eq 0$ is the correct statement in general.

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

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