cn

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suppose A is a complex no. & n belong to N,such that Aⁿ =(A+1)ⁿ=1.then least value of n is,
1.3
2.6
3.9
4.12

#Mathematics #Co-ordinate Geometry

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6 Answers

1

Vivek ·2009-04-04 06:19:19

it is 6 ,try putting Ï‰ in the eqn as it is clear that A is some k^th root of unity

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ANKIT MAHATO ·2009-04-04 06:23:09

yup 6 is the answer !

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Lokesh Verma ·2009-04-04 06:37:47

Aⁿ = (A+1)ⁿ = 1

take mod on both sides

then |A|=|A+1|

thus A lies on bisector of 0 and -1 thus Re(A)=-1/2
|A| = 1 hence Im(A) = Â±√3/2

now see that -1/2Â±√3/2i = e^{i pi/3}

now does it make the answer obvious?

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vaishnavi bansal ·2009-04-04 06:53:06

can u plz solve of in terms of omega???

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Vivek ·2009-04-04 11:17:21

using Ï‰,

Ï‰ⁿ=1 implies n =3,6,9 .......

(Ï‰+1)ⁿ=(-Ï‰²)ⁿ = 1 implies n = 6,12,18 .....

so least value is 6

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vaishnavi bansal ·2009-04-05 05:08:57

than q

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