Question

If $| z - 3 + 2i | \leq 4$ 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: $|z-3+2 i| \leq 4 \Rightarrow |z-(3-2 i)| \leq 4$

Now, $\,\,\,|z|_{\max }=O C+C B=O B=\sqrt{13}+4$
Now,$\,\,\,|z|_{\text {mie }}=A C-O C=O A=4-\sqrt{13}$
Therefore,$\,\,\,|z|_{\max }-|z|_{\min }=(4+\sqrt{13})-(4-\sqrt{13})=2 \sqrt{13}$