Q

# 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)

$\sqrt{13}$

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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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