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Quantitative Ability

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Question

For all complex numbers $z_{1}, z_{2}$ satisfying $| z_{1} | = 12, | z_{2} - 3 - 4 i | = 5,$ the minimum value of $| z_{1} - z_{2} |$ is

A

0

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B

7

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C

2

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D

17

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Solution

The correct option is C 2
We have, $| z_{1} | = 12$ . Therefore $z_{1}$ lies on the circle with centre $(0, 0)$ and radius $12$ units and $| z_{2} - 3 - 4 i |$ is a circle with centre $(3, 4)$ and radius $5$ units.

From above figure it is clear that $| z_{1} - z_{2} |$ , i.e. distance between $z_{1}$ and $z_{2}$ will be minimum when they lie at 𝐴 and 𝐵 respectively.
Then, $| z_{1} - z_{2} | = A B = O A - O B = 12 - 2 \times 5 = 2$

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Quantitative Ability

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