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Properties of Modulus

Let Z1=3+4i a...

Question

Let $Z_{1}$ =3+4i and | $Z_{2}$ |=1, then

A

maximum value of | $Z_{1}$ + $Z_{2}$ | is 6

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B

Maximum value of | $Z_{1}$ + $Z_{2}$ | is 7

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C

Minimum value of | $Z_{1}$ + $Z_{2}$ | is 4

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D

Minimum value of | $Z_{1}$ + $Z_{2}$ | is 3

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Solution

The correct option is C
Minimum value of | $Z_{1}$ + $Z_{2}$ | is 4

Maximum value of | $Z_{1}$ + $Z_{2}$ | is | $Z_{1}$ |+ | $Z_{2}$ | and the minimum value is | | $Z_{1}$ |- | $Z_{2}$ | |
$\Rightarrow$ 5+1 and 5-1
$\Rightarrow$ 6 and 4

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Similar questions

Let $Z_{1}$ =3+4i and | $Z_{2}$ |=1, then

z_{1} = 3 + 4 i

z_{2} = - 4 + 3 i

. Then the modulus of

z = z_{1} + z_{2}

z_{1}

z_{2}

be two complex numbers satisfying

| z_{1} | = 9

| z_{2} - 3 - 4 i | = 4

. Then the minimum value of

| z_{1} - z_{2} |

z_{1}

z_{2}

be two complex numbers satisfying

| z_{1} | = 9

| z_{2} - 3 - 4 i | = 4

. Then the minimum value of

| z_{1} - z_{2} |

z_{1}

z_{2}

be two complex numbers such that

| z_{1} | = 12

| z_{2} - 3 - 4 i | = 5.

Then the minimum value of

| z_{1} - z_{2} |

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