Question

If $|z-3+2i|\le 4$ then the difference between the greatest value and the least value of $|z|$ is :

• A. $2\sqrt{13}$
• B. 8
• C. $4+\sqrt{13}$
• D. $\sqrt{13}$

Answer 1

Answer: (A)

Given: $|z-3+2i|\le 4\Rightarrow |z-(3-2i)|\le 4$

Now, $|z{|}_{\max }=OC+CB=OB=\sqrt{13}+4$
Now,$|z{|}_{\text{mie }}=AC-OC=OA=4-\sqrt{13}$
Therefore,$|z{|}_{\max }-|z{|}_{\min }=(4+\sqrt{13})-(4-\sqrt{13})=2\sqrt{13}$