JEE Main 2019 (Online) 11th January Evening ShiftQuestion 1
Let $z$ be a complex number such that $|z|+z=3+i$ (where $i=\sqrt{-1}$). Then $|z|$ is equal to :
Complex Numbers
Solution
Imaginary parts give $z=x+i$; then $\sqrt{x^2+1}=3-x$, so $x=\frac43$ and $|z|=3-\frac43=\frac53$.