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Properties of Modulus

The minimum v...

Question

The minimum value of $| z - 1 | + | z - 3 |$ is

A

4

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B

2

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C

0

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D

1

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Solution

The correct option is B $2$
We know that,
$| z_{1} | + | z_{2} | \geq | z_{1} - z_{2} |$

$∴ | z - 1 | + | z - 3 | \geq | (z - 1) - (z - 3) | \Rightarrow | z - 1 | + | z - 3 | \geq 2$

Hence minimum value of $| z - 1 | + | z - 3 |$ is $2.$

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Properties of Modulus

Standard XII Mathematics

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