If Z 1- Z 2- Z 3 are complex numbers such that - Z 1- Z 2- Z 3-1- Z 1-1- Z 2-1- Z 3-1 then - Z 1- Z 2- Z 3- isA- 3B- -3C- -1D-

The correct option is D 1 |Z_1+Z_2+Z_3|=|1/Z_1+1/Z_2+1/Z_3|=1 ...

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Complex Numbers

If Z 1, Z 2, ...

Question

If $Z_{1}, Z_{2}, Z_{3}$ are complex numbers such that

$| Z_{1} | = | Z_{2} | = | Z_{3} | = | \frac{1}{Z_{1}} + \frac{1}{Z_{2}} + \frac{1}{Z_{3}} | = 1$ then $| Z_{1} + | Z_{2} + Z_{3} |$ is

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z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} | = ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ = 1,

| z_{1} + z_{2} + z_{3} |

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} | = ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1

| z_{1} + z_{2} + z_{3} |

If $z_{1}, z_{2} a n d z_{3}$ are complex numbers such that

| $z_{1}$ |=| $z_{2}$ |=| $z_{3}$ |= $∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ = 1$ ,

then | $z_{1}$ + $z_{2}$ + $z_{3}$ |

z_{1,} z_{_{2},} z_{3}

| z_{1} | = | z_{2} | =

| z_{3} |

∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1,

| z_{1 +} z_{2} + z_{3} |

z_{1}, z_{2}

z_{3}

| z_{1} | = | z_{2} | = | z_{3} | = ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1

| z_{1} + z_{2} + z_{3} |

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