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If `alpha, beta in C` are the distinct roots of the equation `x^(2)-x+1=0`, then `alpha^(101)+beta^(107)` is equal to

A

0

B

1

C

2

D

`-1`

Text Solution

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The correct Answer is:
B
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DISHA PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Exercise -2 : Concept Applicator
  1. If alpha, beta in C are the distinct roots of the equation x^(2)-x+1=0...

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  2. If z1=sqrt2 (cospi/4+isin(pi/4)) and z2=sqrt3(cospi/3+isin(pi/3)) then...

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  3. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

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  4. Write the complex number z = (i-1)/(cos pi/3 + i sin pi/3)in polar fo...

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  5. A variable complex number z=x+iy is such that arg(z-1)/(z+1)= pi/2. S...

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  6. If arg(z) lt 0, then find arg(-z) -arg(z).

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  7. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (|z|)/2 (b) |z| ...

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  8. If z=x+i y, z^(1/3)=a-i b " and " x/a-y/b=lambda(a^2-b^2), then lambda...

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  9. Amplitude of (1+sqrt3i)/(sqrt3+1)is

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  10. If z=(3-i)/(2+i)+(3+i)/(2-i) then value of arg (zi) is

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  11. If (y^2-5y+3)(x 62+x+1)<2x for all x in R , then fin the interval in ...

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  12. Let x+1/x=1 and a, b and c are distict positive integer such that (x^(...

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  13. If z=(3+7i)(a+ib), where a, b in Z-{0}, is purely imaginery, then mini...

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  14. The value of lambda for which the sum of squares of roots of the equat...

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  15. The set of all real numbers x for which x^2-|x+2| +x gt 0 is

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  16. If alpha,beta are the roots of the equation ax^2+ bx +c =0, then alp...

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  17. If log(1/2) ((x^2+6x+9)/(2(x+1)) )< - log2(x+1) then complete set of v...

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  18. Solve: x^(2) + 2 = 0

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  19. If a<b<c<d , then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 a...

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  20. If the cube roots of unity are 1,w w^2,then the roots of the equation ...

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  21. Find t values of the parameter a such that the rots alpha,beta of the ...

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