Let $z$ be a complex number such that $|z|+z=3+i, i=\sqrt{-1}$, then $|z|$ is equal to

Question

Aicharya · Accepted Answer

$\begin{aligned} & |z|+z=3+i \ & \Rightarrow \sqrt{x^2+y^2}+x+i y=3+i[	ext { let } z=x+i y] \ & \Rightarrow \sqrt{x^2+y^2}+x=3 	ext { and } y=1 \ & \Rightarrow \sqrt{x^2+1^2}+x=3 \ & \Rightarrow x^2+1=(3-x)^2 \ & \Rightarrow x=\frac{4}{3} \ & \Rightarrow|z|=\sqrt{x^2+y^2}=\sqrt{\left(\frac{4}{3}ight)^2+1^2}=\frac{5}{3}\end{aligned}$

Let $z$ be a complex number such that $|z|+z=3+i, i=\sqrt{-1}$, then $|z|$ is equal to

Solution