If |z_1|=1, , |z_2| =2, ,|z_3|=3 and |9z_1z_2 | vedclass

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Question

$\left|z_{1}\right|^{2}=1 \Rightarrow z_{1} \bar{z}_{1}=1,\left|z_{2}\right|^{2}=4 \Rightarrow z_{2} \bar{z}_{2}=4$

$\left|z_{3}\right|^{2}=9 \Righ

Vedclass · Accepted Answer

$2$

Vedclass · Answer

$\left|z_{1}\right|^{2}=1 \Rightarrow z_{1} \bar{z}_{1}=1,\left|z_{2}\right|^{2}=4 \Rightarrow z_{2} \bar{z}_{2}=4$

$\left|z_{3}\right|^{2}=9 \Rightarrow z_{3} \bar{z}_{3}=9$

$\left|9 z_{1} z_{2}+4 z_{1} z_{3}+z_{2} z_{3}\right|=12$

$\left|z_{3} \bar{z}_{3} z_{1} z_{2}+z_{2} \bar{z}_{2} z_{1} z_{3}+z_{1} \bar{z}_{1} z_{2} z_{3}\right|=12$

$\Rightarrow\left|z_{1}\right|\left|z_{2}\right|\left|z_{3}\right|\left|\bar{z}_{1}+\bar{z}_{2}+\bar{z}_{3}\right|=12$

$\Rightarrow\left|\bar{z}_{1}+\bar{z}_{2}+\bar{z}_{3}\right|=2 \Rightarrow\left|z_{1}+z_{2}+z_{3}\right|=2$

If $|z_1|=1, \, |z_2| =2, \,|z_3|=3$ and $|9z_1z_2 + 4z_1z_3+z_2z_3| =12$ then the value of $|z_1+z_2+z_3|$ is equal to :-

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