question_answer

If  z be a complex number satisfying \[|\operatorname{Re}(z)|+|lm(z)|\,=4,\] then \[|z|\] cannot be [JEE MAIN Held on 09-01-2020 Evening]

A) \[\sqrt{10}\]

B) \[\sqrt{8}\]

C) \[\sqrt{\frac{17}{2}}\]

D) \[\sqrt{7}\]

Correct Answer: D

Solution :

\[z=x+iy\] \[A\text{/}Q\,\,\,|x|+|y|\,\,=4\] Min. \[|z|\,=2\sqrt{2}\]  Max. \[|z|\,=\,\,4\] so  \[|z|\,\in \,\,\left[ 2\sqrt{2},\,4 \right]\] \[\Rightarrow \,\,\,|z|\,\ne \,\,\sqrt{7}\]