Question:
Let $z$ be a complex number such that $|z|+z=3+i($ where $i=\sqrt{-1})$. Then $|z|$ is equal to :-
Correct Option: , 4
Solution:
$|z|+z=3+i$
$z=3-|z|+i$
Let $3-|z|=a \Rightarrow|z|=(3-a)$
$\Rightarrow \mathrm{z}=\mathrm{a}+\mathrm{i} \Rightarrow|\mathrm{z}|=\sqrt{\mathrm{a}^{2}+1}$
$\Rightarrow 9+a^{2}-6 a=a^{2}+1 \Rightarrow a=\frac{8}{6}=\frac{4}{3}$
$\Rightarrow|z|=3-\frac{4}{3}=\frac{5}{3}$
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