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Properties of Modulus

For all compl...

Question

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

A

2

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B

7

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C

17

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Solution

The correct option is A 2
The point $z_{1}$ and $z_{2}$ describe circles of radii 12, 5 with centres O and (3, 4). The nearest distance between the circles is 12 - 10 = 2.

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