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Properties of Modulus

If | z 1-1|<2...

Question

If $| z_{1} - 1 | < 2, | z_{2} - 2 | < 1,$ then maximum possible integral value of $| z_{1} + z_{2} |$ is

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Solution

The correct option is C $5$
$| z_{1} + z_{2} | = | z_{1} - 1 + z_{2} - 2 + 3 | \leq | z_{1} - 1 | + | z_{2} - 2 | + 3$
$\Rightarrow | z_{1} + z_{2} | < 2 + 1 + 3$
$∴ | z_{1} + z_{2} | < 6$
So, maximum possible integral value of $| z_{1} + z_{2} |$ is $5$

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Properties of Modulus

Standard XII Mathematics

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If |z1−1|<2,|z2−2|<1, then maximum possible integral value of |z1+z2| is

The correct option is C 5|z1+z2|=|z1−1+z2−2+3|≤|z1−1|+|z2−2|+3 ⇒|z1+z2|<2+1+3 ∴|z1+z2|<6 ​​​​​So, maximum possible integral value of |z1+z2| is 5

If $| z_{1} - 1 | < 2, | z_{2} - 2 | < 1,$ then maximum possible integral value of $| z_{1} + z_{2} |$ is

The correct option is C $5$
$| z_{1} + z_{2} | = | z_{1} - 1 + z_{2} - 2 + 3 | \leq | z_{1} - 1 | + | z_{2} - 2 | + 3$
$\Rightarrow | z_{1} + z_{2} | < 2 + 1 + 3$
$∴ | z_{1} + z_{2} | < 6$
So, maximum possible integral value of $| z_{1} + z_{2} |$ is $5$