Question

Let z be a complex number such that $|z|+z=3+i$ (where $i$ = $\sqrt{-1)}.$ Then $|z|$ is equal to:-

• A. $\frac{5}{4}$
• B. $\frac{\sqrt{4}1}{4}$
• C. $\frac{\sqrt{3}4}{3}$
• D. $\frac{5}{3}$

Answer 1

The correct option is D $\frac{5}{3}$

$|z|+z=3+i$

$z=3-|z|+i$

Let $3-|z|=a⟹|z|=(3-a)$

$⟹z=a+i⟹|z|=\sqrt{a^2+1}$

$⟹9+a^2-6a=a^2+1⟹a=\frac{8}{6}=\frac{4}{3}$
$⟹|z|=3-\frac{4}{3}=\frac{5}{3}$