Let z be a complex number such that -z-i-2- If z1-5-3i- then the maximum value of -iz-z1- is

Given: |z i|≤2 and z_1=5+3i Now, nbsp; |iz+z_1|=|iz+5+3i| =|z+3 5i| =|(z i)+(3 4i)| ≤|z i|+|3 4i| ≤2+5 i.e., |iz+z_1|≤7 ∴ The maximum value of |iz+z_1| is 7 ...

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Byju's Answer

Standard XII

Mathematics

Complex Plane

Let z be a co...

Question

Let $z$ be a complex number such that $| z - i | \leq 2.$ If $z_{1} = 5 + 3 i,$ then the maximum value of $| i z + z_{1} |$ is

7 + \sqrt{13}

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7 + \sqrt{12}

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7

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9

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Solution

The correct option is C $7$
Given: $| z - i | \leq 2$ and $z_{1} = 5 + 3 i$
Now,
$| i z + z_{1} | = | i z + 5 + 3 i |$
$= | z + 3 - 5 i |$
$= | (z - i) + (3 - 4 i) |$
$\leq | z - i | + | 3 - 4 i |$
$\leq 2 + 5$
i.e., $| i z + z_{1} | \leq 7$
$∴$ The maximum value of $| i z + z_{1} |$ is $7$

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Let z be a complex number such that |z−i|≤2. If z1=5+3i, then the maximum value of |iz+z1| is

The correct option is C 7Given: |z−i|≤2 and z1=5+3i Now, |iz+z1|=|iz+5+3i| =|z+3−5i| =|(z−i)+(3−4i)| ≤|z−i|+|3−4i| ≤2+5 i.e., |iz+z1|≤7 ∴ The maximum value of |iz+z1| is 7

Let $z$ be a complex number such that $| z - i | \leq 2.$ If $z_{1} = 5 + 3 i,$ then the maximum value of $| i z + z_{1} |$ is

The correct option is C $7$
Given: $| z - i | \leq 2$ and $z_{1} = 5 + 3 i$
Now,
$| i z + z_{1} | = | i z + 5 + 3 i |$
$= | z + 3 - 5 i |$
$= | (z - i) + (3 - 4 i) |$
$\leq | z - i | + | 3 - 4 i |$
$\leq 2 + 5$
i.e., $| i z + z_{1} | \leq 7$
$∴$ The maximum value of $| i z + z_{1} |$ is $7$