The minimum value of - z -1- z -3- isA- 4B- 0C- 2D- 1

We know that, |z_1|+|z_2| ≥|z_1 z_2| ∴ |z 1|+|z 3| ≥|(z 1) (z 3)| ⇒ |z 1|+|z 3| ≥2 Hence, the minimum value of |z 1|+|z 3| is 2. ...

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Standard XII

Mathematics

Properties of Modulus

The minimum v...

Question

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

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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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[IIT Screening 2002]

$| z_{1} | = 1, | z_{2} | = 2, | z_{3} | = 3 a n d | 9 z_{1} z_{2} + 4 z_{1} z_{3} + z_{2} z_{3} | = 12$ , then the value of $| z_{1} + z_{2} + z_{3} |$ is equal to

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Properties of Modulus

Standard XII Mathematics

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The minimum value of |z−1|+|z−3| is

The correct option is B 2We know that, |z1|+|z2|≥|z1−z2| ∴|z−1|+|z−3|≥|(z−1)−(z−3)|⇒|z−1|+|z−3|≥2 Hence minimum value of |z−1|+|z−3| is 2.

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

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 $2.$