Compleksh::::

JEE Advanced 2015 Papers › Algebra questions › Compleksh::::

let Z_r,r=1,2,3.....n are n distinct roots of eq ^{n}C_{1}x+^{n}C_{2}x^{2}+^{n}C_{3}x^{3}+.......^{n}C_{n}x^{n}=0 in argand plane.If der exist exactly one Z_r, rÎµ{1,2....n} such that arg\left(\frac{Z_{r}-(-1+\sqrt{2}i}{(-1)-(-1+\sqrt{2}i)} \right)=\frac{\pi }{4} then n can be ??

#Mathematics #Algebra

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4 Answers

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Hari Shankar ·2010-01-15 21:04:50

pls check the denominator of the arg expression

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Che ·2010-01-15 21:14:30

i checked the denominator......no prob with it.

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Kalyan Pilla ·2010-01-15 21:47:47

is the same as (x+1)ⁿ=1

The solution to this lies on the red circle in the fig.

z_r is a point such that, arg(-1+√2i - z_r)=âˆ©/4

This when solved, along with the eqn of circle, |z+1|=1 or by using simple geometry gives z_r= e^i3âˆ©/4-1

This when substituted in the eqn gives, (e^i3âˆ©/4)^n/r=1

=> 3âˆ©n/4 = 2âˆ© , or n/r=8/3,

This gives n=8 and e^i3âˆ©/4-1 is the third root anti-clockwise...........

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Che ·2010-01-15 22:18:34

yes correct !

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