C.N.'

JEE Main 2015 Sample Questions › Algebra questions › C.N.'

Let a,bER and 0<a<1 and 0<b<1 if z₁=-a+i,z₂=-1+bi and z₃0 and z₁,z₂,z₃ form an equilateral triangle then
(A) (a+√3)(b+√3)=4
(B)a²-2a-2b=0
(C)(a-2)(b-2)=3
(D)a⁴-4(a+b)²=0.

#Mathematics #Algebra

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3 Answers

Joydoot ghatak ·2011-03-14 02:58:59

FOR equilateral triangle,

z₁² + z₂² + z₃² - z₁z₂ - z₂z₃ - z₃z₁ = 0

and
(z₁ + z₂w + z₃w²) (z₁ + z₂w² + z₃w) = 0.

use this...
might help.. :)

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Joydoot ghatak ·2011-03-16 08:23:55

found a simplier method.. :)

z₂ - z₃z₁- z₃ = e^iâˆ‚
here âˆ‚=60Â° (as triangle is equilateral).

thus,e^iâˆ‚ = cosâˆ‚ +isinâˆ‚ = 1+√3i
2.

thus,
-1 + bi-a + i = 1+√3i2.

thus,on simplifying.
-2+2bi = -√3ai - √3 - a +i.

equating the real and imaginary co-efficients weget,
a=b= 2 - √3

thus...
i get (A) and (C) as answer..

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Vinay Arya ·2011-03-16 20:13:32

Yes you are getting the right answers.
Thank you very much.

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C.N.'

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