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If omega is a cube root of unity, prove ...

If `omega` is a cube root of unity, prove that
`(1+omega-omega^2)^3-(1-omega+omega^2)^3=0`

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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. If omega is a non-real cube root of unity, then the value of (1-omega...

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  2. If omega is an imaginary cube root of unity then prove that If omeg...

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  3. If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1...

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  4. If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+...

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  5. If omega is a cube root of unity, then find the value of the following...

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  6. If =a+b,y=aomega+bomega^2 and z=aomega^2+bomega, prove tht xyz=a^3+b^3

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  7. If x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega where omega is an i...

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  8. 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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  9. (1+w)^7=A+Bw where w is the imaginary cube root of of a unity and A, B...

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

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

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

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

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

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  15. Interpret the following locii in z in C

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

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

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

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

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

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