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

Question

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

Accepted Answer

Let z = x + iy

given that |Re(z)| + |Im(z)| = 4

$$ \therefore $$ |x| + |y| = 4

Maximum value of |z| = 4

Minimum value of |z| = perpendicular distance of line AB from (0, 0) = $$2\sqrt 2 $$

$$ \therefore $$ |z| $$ \in $$ $$\left[ {2\sqrt 2 ,4} \right]$$

$$ \therefore $$ |z| cannot be $$\sqrt {7} $$.

Solutions · 1