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)

$\sqrt{7}$

Answer 2

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