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The value of the expression , (2-w)(2-w^...

The value of the expression , `(2-w)(2-w^2)+2.(3-w)(3-w^2)+....... ...... +(n-1).(n-w)(n-w^2)`, where w is an imaginary cube root of unity is

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The correct Answer is:
`[(n(n+1))/2]^2-n`
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The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+1/omega^(2))+(3+1/omega)(3+1/omega^(2))+…………..+(n+1/omega)(n+1/omega^(2)) , where omega is an imaginary cube root of unity, is

MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. 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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  2. (1+w)^7=A+Bw where w is the imaginary cube root of of a unity and A, B...

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  3. The value of the expression , (2-w)(2-w^2)+2.(3-w)(3-w^2)+....... .......

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  4. If w is an imaginary cube root of unity then prove that (1...

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  5. If w is an imaginary cube root of unity then prove that I...

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  6. Interpret the following locii in z in C. 1lt|z-2i|lt3

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  7. Interpret the following locii in z in C. Im (z)ge1

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  8. Interpret the following locii in z in C

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  9. If |z – 2 + i| ge2, then find the greatest and least value of |z|.

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  10. If |z + 3| le 3 then find minimum and maximum values of |z|

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  11. If |z + 3| le 3 then find minimum and maximum values of |z-1|

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  12. If |z + 3| le 3 then find minimum and maximum values of |z+1|

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  13. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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  14. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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  15. The region represented by RE(z)<=2, Im(z)<=2 and pi/8<=arg(z)<=(3pi)/8...

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  16. Let I Arg((z-8i)/(z+6))=pmpi/2 II: Re ((z-8i)/(z+6))=0 Show that ...

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  17. if a and bbetween 0 and 1 such that the points (a, 1). (1, b) and (0, ...

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  18. Find the non-zero complex numbers z satisfying z =i z^2dot

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  19. If the complex numbers z1, z2,.......zn lie on te unit circle |z| = 1 ...

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  20. Find the Cartesian equations of the locus of z in the complex plane sa...

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