If -z- 3- then the least value of -z - 14 - is

The correct option is B 114 |z + 14 | = |z ( 14 ) | ≥ |z| | 14 | ⇒ #160; |(z) ( 14) |≥ 3 | 14 | = 114 ∴ |z + 14 | ≥114 ...

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Standard XII

Mathematics

Definition of Functions

If |z|≥ 3, ...

Question

If $| z | \geq 3$ , then the least value of $∣ ∣ ∣ z + \frac{1}{4} ∣ ∣ ∣$ is

\frac{11}{2}

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\frac{11}{4}

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3

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\frac{1}{4}

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Solution

The correct option is B $\frac{11}{4}$
$∣ ∣ ∣ z + \frac{1}{4} ∣ ∣ ∣$
$= ∣ ∣ ∣ z - (\frac{- 1}{4}) ∣ ∣ ∣ \geq | z | - ∣ ∣ ∣ \frac{- 1}{4} ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ (z) - (\frac{- 1}{4}) ∣ ∣ ∣ \geq 3 - ∣ ∣ ∣ \frac{1}{4} ∣ ∣ ∣ = \frac{11}{4}$
$∴ ∣ ∣ ∣ z + \frac{1}{4} ∣ ∣ ∣ \geq \frac{11}{4}$

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If |z|≥3, then the least value of ∣∣∣z+14∣∣∣ is

The correct option is B 114∣∣∣z+14∣∣∣=∣∣∣z−(−14)∣∣∣≥|z|−∣∣∣−14∣∣∣⇒∣∣∣(z)−(−14)∣∣∣≥3−∣∣∣14∣∣∣=114∴∣∣∣z+14∣∣∣≥114

If $| z | \geq 3$ , then the least value of $∣ ∣ ∣ z + \frac{1}{4} ∣ ∣ ∣$ is