Let and . Then the minimum value of is : [2025]

Question

Let $| z_{1} - 8 - 2 i |$ $\leq 1$ and $| z_{2} - 2 + 6 i |$ $\leq 2, z_{1}, z_{2} \in C$ . Then the minimum value of $| z_{1} - z_{2} |$ is : [2025]

Smart Achievers · Accepted Answer

(3)

$A B = \sqrt{{(8 - 2)}^{2} + {(2 + 6)}^{2}} = \sqrt{100} = 10$

$∴$ $| z_{1} - z_{2} |_{\min}$ $= 10 - 2 - 1 = 7$

Solution

Q.
Let $| z_{1} - 8 - 2 i |$ $\leq 1$ and $| z_{2} - 2 + 6 i |$ $\leq 2, z_{1}, z_{2} \in C$ . Then the minimum value of $| z_{1} - z_{2} |$ is : [2025]

1 13

2 3

3 7

4 10

Ans.
(3)

$A B = \sqrt{{(8 - 2)}^{2} + {(2 + 6)}^{2}} = \sqrt{100} = 10$

$∴$ $| z_{1} - z_{2} |_{\min}$ $= 10 - 2 - 1 = 7$

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