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Properties of Modulus

If z1 =24+7i ...

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} |

Q. The greatest and least value of

| z_{1} + z_{2} |

z_{1} = 24 + 7 i

| z_{2} | = 6

are respectively

Q. Find the greatest and the least value of

| z_{1} + z_{2} |

z_{1} = 24 + 7 i

| z_{2} | = 6.

Q. The greatest and the least value of

| z_{1} + z_{2} |

z_{1} = 24 + 7 i

| z_{2} | = 6

are respectively

Q. Assertion :If

z_{1}

z_{2}

be two complex numbers such that

| z_{1} | = | z_{2} | + | z_{1} - z_{2} |

(\frac{z_{1}}{z_{2}}) = 0

. Reason: arg (z) = 0

\Rightarrow z

lies on x - axis.

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Properties of Modulus

Standard XIII Mathematics

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