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If z1, z2 be the complex numbers satisfy...

If `z_1, z_2` be the complex numbers satisfying `x^2`+4=2x, prove that `z_1^n+z_2^n=2^(n+1) cosfrac(npi)(3)` .

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If 2cos A = x+1/x , 2cosbeta=y+1/y then show that 2cos(A-B) =x/y+y/x.

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  2. If xn =cos ((pi)/(2^(n)))+isin((pi)/(2^(n)))Prove that x1 x2…..xoo=-1

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  3. If z1, z2 be the complex numbers satisfying x^2+4=2x, prove that z1^n+...

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  4. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

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  5. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

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  6. If z^7+1 =0 then cos(pi/7) cos((3pi)/7) cos((5pi)/7) is (A) 1/8 ...

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  7. Hence deduce that cos(pi)/(9)cos(2 pi)/(9)cos(3 pi)/(9)cos(4 pi)/(9)=(...

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  8. (2+omega+omega^2)^3+(1+omega-omega^2)^3=(1-3omega+omega^2)^4=1

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  9. (i) If alpha,beta be the imaginary cube root of unity, then show that ...

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  10. If x=a+b,y=aomega+bomega^2 nd z=omega^2+bomega, prove that x^3+y^3+z^3...

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  11. If x = a + b, y= aw + bw^2 and z = aw^2 + bw, where w is an imaginary ...

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  12. Prove that ((i+sqrt3)/2)^100+((i-sqrt3)/2)^100+1=0.

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  13. What is the value of ((i+sqrt3)/(-i+sqrt3))^(200)+((i-sqrt3)/(i+sqrt3)...

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  14. Prove that sqrt(-1-sqrt(-1-sqrt1-… prop=w or w^2 .

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  15. Resolve into the linear factor: a^3+b^3

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  16. Resolve into the linear factor: a^3+b^3+c^3-3abc

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  17. value of the series a(0)-a(2) + a(4)-a(6) +….. is

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  18. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a1-a3+a5-a7+… .

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  19. If (1+x)^n=a0+a1x+a2x^2+...+anx^n then find : a0+a3+a6+a9+… .

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  20. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

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