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Algebra

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Post:	2173

8 Jun 2008 15:20:52 IST

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340

Complex Numbers

None

satisfy

and

$z_1+z_2+z_3 = \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3}$

Prove that atleast one of equals 1

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SUNDEEP ALLAMRAJU

Blazing goIITian

Joined: 28 Feb 2008

Posts: 1014

8 Jun 2008 16:06:31 IST

Like 7 people liked this

1/z₁+1/z₂+1/z₃=z₁z₂+z₂z₃+z₃z₁[as z₁z₂z₃=1]=a(say)

Then,z₁,z₂,z₃ are the roots of the 3rd degree equation,

z³-az²+az-1=0 for which 1 is always a root.So,Atleast one of z_i equals 1.[when a=0,all the roots are 1 only.]

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