JEE Main 2020 (Online) 9th January Evening ShiftQuestion 1
If $z$ be a complex number satisfying $|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4$, then $|z|$ cannot be :
Complex Numbers
Solution
$|x|+|y|=4$: $x^2+y^2=16-2|x||y|$ with $|x||y|\in[0,4]$, so $|z|^2\in[8,16]$. $\sqrt7$ has $|z|^2=7<8$, impossible. Answer: (A).