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If 1,omega, omega^2 are the three cube r...

If `1,omega, omega^2` are the three cube roots of unity, prove that `(1+omega^2)^4=omega`.

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L.H.S`=(1+omega^2)^4=(-omega)^4=omega^4`
`=omega^3.omega=1.omega=omega`
="R.H.S.(Proved)"
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MBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Express 1+isqrt2=r cos theta +sin theta complex numbers in the polar ...

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  2. Express isqrt3 =rcos theta +ir sin theta complex numbers in the polar...

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  3. If 1,omega, omega^2 are the three cube roots of unity, prove that (1+o...

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

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  5. (1-omega)(1-omega^2)(1-omega^4)(1-omega^5)=9

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  6. (2+5omega +2 omega^2)^6=(2+2omega+5 omega^2)^6=729

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  7. (1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^2)….to 2n Factor...

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  8. Prove that x^3+y^3+z^3-3xyz =(x+y+z)(x+omegay+omega^2z)(x+yomega^2+z ...

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  9. If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show thatxyz =a^3+b^3

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  10. If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show that x^2+y^2+z^2...

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  11. If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show thatx^3+y^3+z^3=...

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  12. If ax+by +cz=X,cx+by +az=Y,bx+ay+cz=Z show that (a^2+b^2+c^2-ab-bc-ca...

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  13. If |z1|le1,|z2|le1"show that" |1-z1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2...

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  14. If a, b, c are complex numbers satisfying a+b+c=0 and a^2+b^2+c^2=0 th...

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  15. What do the {z:|z-a|+|z+a|=2c} "where" |a|lt c represent?

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  16. What do the{z:|z-a|-|z+a|=c} represent?

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  17. What happen in (i)|a|ge c?

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  18. Given cos alpha+cos beta +cos gamma=sin alpha+sin beta +sin gamma=0 S...

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  19. Use Binomial theorem and De Moivre's theorem to show cos 3 theta=4 cos...

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  20. Find square root of -5+12sqrt(-1)

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