If -1 - -2- -3 are complex number such that-1 - -2 - -3 - -1-1 -1-2 -1-3 -1-then find the value of-1-2-3 -

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Standard XIII

Mathematics

Many-One into Function

If 𝑧1 , 𝑧2,...

Question

If $z_{1}, z_{2}, z_{3}$ are complex number such that
$| z_{1} | = | z_{2} | = | z_{3} | ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1,$ then find the value of $| z_{1} + z_{2} + z_{3} |$

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Solution

$∵ | z_{1}, z_{2}, z_{3} |$
$∣ ∣ ∣ \frac{1}{_{1}} + \frac{1}{_{2}} + \frac{1}{_{3}} ∣ ∣ ∣$
$∣ ∣ ∣ ∣ ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ ∣$
$∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣$
$= 1$
$T h e r e f o r e | z_{1}, z_{2}, z_{3} | = 1$

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Many-One into Function

Standard XIII Mathematics

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If z1,z2,z3 are complex number such that |z1|=|z2|=|z3|∣∣∣1z1+1z2+1z3∣∣∣=1,then find the value of|z1+z2+z3|

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If $z_{1}, z_{2}, z_{3}$ are complex number such that
$| z_{1} | = | z_{2} | = | z_{3} | ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1,$ then find the value of $| z_{1} + z_{2} + z_{3} |$