Question

If $|z-3+2i|\le 4$ (where $i=\sqrt{-1})$ then the difference of greatest and least value of $|z|$ is

• A. $2\sqrt{11}$
• B. $3\sqrt{11}$
• C. $3\sqrt{5}$
• D. $3\sqrt{13}$

Answer 1

The correct option is C $3\sqrt{5}$

Given,

$|z-3+2i|\le 4$

case I:

$z-3+2i=4$

$z=7-2i$ max

case II:

$-(z-3+2i)=4$

$z=-2-2i$ min

$\sqrt{(7^2+(-2{)}^2)-((-2{)}^2+(-2{)}^2)}$

$=\sqrt{53-8}$

$=\sqrt{45}$

$=3\sqrt{5}$