If $z$ satisfies the equation $| z - 3 i | + | z - 4 | = 5$ , then minimum value of $| z |$ is

5

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12

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\frac{5}{12}

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\frac{12}{5}

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Solution

The correct option is B $5$
$| z - 3 i + z - 4 | \leq | z - 3 i | + | z - 4 |$
$| 2 z - 3 i - 4 | \leq 5$
$| 2 z | - | 3 i + 4 | \leq 5$
$| 2 z | - 5 \leq 5$
$| z | \leq 5$

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Similar questions

Find the complex number z satisfying the equations $∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣$ = $\frac{5}{3}$ , $∣ ∣ \frac{z - 4}{z - 8} ∣ ∣$ =1

∣ ∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣ ∣ = \frac{5}{3}

∣ ∣ ∣ \frac{z - 4}{z - 8} ∣ ∣ ∣ = 1

z_{1}, z_{2}

| z_{1} | = 20

| z_{2} - 5 - 12 i | = 4

| z_{1} - z_{2} |

| z_{1} | = 12

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

| z_{1} - z_{2} |

Find the complex numbers $z$ which simultaneously satisfy the equations

$∣ ∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣ ∣ = \frac{5}{3}$ and $∣ ∣ ∣ \frac{z - 4}{z - 8} ∣ ∣ ∣ = 1$ .

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