Question

If $z$ be a complex number satisfying $\left|Re\left(z\right)\right|+\left|Im\left(z\right)\right|=4,$ then $|z|$ cannot be :

• A. $\sqrt{7}$
• B. $\sqrt{\frac{17}{2}}$
• C. $\sqrt{10}$
• D. $\sqrt{8}$

Answer 1

Answer: (A)

$z=x+iy|x|+|y|=4$
$\left|z\right|=\sqrt{x^2+y^2}\Rightarrow {\left|z\right|}_{min}=\sqrt{8}\&{\left|z\right|}_{max}=4=\sqrt{16}$
So |z| cannot be $\sqrt{7}$