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Properties of Modulus

If z1=24+7 i ...

Question

If $z_{1} = 24 + 7 i$ and $| z_{2} | = 6$ then $| z_{1} + z_{2} |$ lies in

A

[12, 25]

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B

[19, 31]

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C

[6, 25]

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D

[13, 37]

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Solution

The correct option is B $[19, 31]$
Given, $z_{1} = 24 + 7 i \Rightarrow | z_{1} | = \sqrt{24^{2} + 7^{2}} = 25$
and $| z_{2} | = 6$
We know that
$| | z_{1} | - | z_{2} | | \leq | z_{1} + z_{2} | \leq | z_{1} | + | z_{2} | \Rightarrow | 25 - 6 | \leq | z_{1} + z_{2} | \leq 25 + 6 \Rightarrow 19 \leq | z_{1} + z_{2} | \leq 31$

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Similar questions

z_{1} = 24 + 7 i

| z_{2} | = 6

| z_{1} + z_{2} |

z_{1} \neq - z_{2}

| z_{1} + z_{2} | = ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} ∣ ∣ ∣

z_{1} = \sqrt{3} + i \sqrt{3}

z_{2} = \sqrt{3} + i

then the complex number

\frac{z_{1}}{z_{2}}

lies in the quadrant number :

z_{1} = (2 - i)

z_{2} = (1 + i),

∣ ∣ ∣ \frac{z_{1} + z_{2} + 1}{z_{1} - z_{2} + i} ∣ ∣ ∣

z_{1} = (2 - i)

z_{2} = (1 + i),

∣ ∣ ∣ \frac{z_{1} + z_{2} + 1}{z_{1} - z_{2} + i} ∣ ∣ ∣

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Properties of Modulus

Standard XII Mathematics

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