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I have a doubt, kindly clarify. - Complex numbers and quadratic equations - JEE Main-7

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

  • Option 1)

    2\sqrt{13}

  • Option 2)

    8

  • Option 3)

    4+\sqrt{13}

  • Option 4)

    \sqrt{13}

 
Answers (1)
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As we learned

Let's solve this problem geometrically

Here r = 4

So minimum value of \left | 2 \right |= 4-\sqrt{13}

and max. value = 4+\sqrt{13}

Difference = = 4+\sqrt{13}-\left (4-\sqrt{13} \right )=2\sqrt{13} 

 


Option 1)

2\sqrt{13}

Option 2)

8

Option 3)

4+\sqrt{13}

Option 4)

\sqrt{13}

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