JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z\) be a complex number satisfying \(|\operatorname{Re}(z)|+|\operatorname{Im}(z)|=4,\) then \(|z|\) cannot be
- A \(\sqrt{\frac{17}{2}}\)
- B \(\sqrt{10}\)
- C \(\sqrt{8}\)
- D \(\sqrt{7}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{7}\)
Step-by-step Solution
Detailed explanation
\(z=x+i y\) \(|x|+|y|=4\) \(|z|=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}} \Rightarrow|\mathrm{z}|_{\min }=\sqrt{8} \&|\mathrm{z}|_{\max }=4=\sqrt{16}\) So \(|z|\) cannot be \(\sqrt{7}\)
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