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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

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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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Similar questions

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

z_{1}, z_{2}

| z_{1} | = 12

| z_{2} - 3 - 4 i | = 5

| z_{1} - z_{2} |

z_{1}, z_{2}

| z_{1} | = 12; | z_{2} - 3 - 4 i | = 5

| z_{1} - z_{2} |

z_{1}, z_{2}

| z_{1} | = 12

| z_{2} - (3 + 4 i) | = 5

| z_{1} - z_{2} |

z_{1}, z_{2}

| z_{1} | = 12

| z_{2} - 3 - 4 i | = 5

| z_{1} - z_{2} |

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