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Solve x^9-x^5+x^4-1=0...

Solve `x^9-x^5+x^4-1=0`

A

`cispi/5,cis(3pi)/(5),cispi,cis(7pi)/(5),cis(9pi)/(5),pm 1,pm i`

B

`cispi/3,cis(2pi)/(3),cispi,cis(7pi)/(3),cis(9pi)/(3),pm 1`

C

`cispi/2,cis(3pi)/(2),cispi,cis(7pi)/(2),cis(9pi)/(2),pm 1`

D

`1,i,cispi/2,cis(3pi)/(2),cispi,cis(7pi)/(2)`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. All the values of (-i)^(1//3) are given by

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  2. If x^4-1=0 then x=

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  3. Solve x^9-x^5+x^4-1=0

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  4. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

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  5. If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, the...

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  6. A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^...

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  7. Assertion (A): If A, B, C are the angles of a triangle such that cos A...

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  8. IF omega represents a complex cube root of unity, then (1+1/omega)(1+1...

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  9. Assertion (A) : If alpha=cos((2pi)/(7))+isin((2pi)/(7)),p=alpha+alpha^...

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  10. If z=(sqrt3-i)/(2) then (i^(101)+z^(101))^(103)=

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  11. The roots of (z-1)^n=i(z+1)^n are plotted on the argand plane they are

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  12. If 'alpha' be the non-real n^(th) roots of unity, then 1+3alpha+5alpha...

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  13. If cos alpha+2cos beta+3cos gamma=sinalpha+2sinbeta+3singamma=0 then s...

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  14. If sin(A+iB)=x+iy then ((x^2)/(sin^2A)-(y^2)/(cos^2A))+((x^2)/(cosh^2B...

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  15. I : sum(k=1)^(6)[sin((2kpi)/(7))-icos((2kpi)/(7))]=i II : sum(r=1)...

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  16. Match the following. {:(Column-I," "Column-II),(I" : "x=costheta...

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  17. The ascending order of the values of z1(1+i)^4+(1-i)^4, z2=(sq...

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  18. I : Value of i^i=e^(-pi/2) II : z=ilog(2+sqrt3) then sinz=2 wh...

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  19. Assertion (A) : (Costheta+iSintheta)^(10)+(Costheta-iSintheta)^(10)=2c...

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  20. The modulus argument form of 1+iTantheta when theta epsilon (pi/2,pi) ...

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