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If x=a+b, y= a alpha+b beta and z=a beta...

If `x=a+b, y= a alpha+b beta and z=a beta+balpha" "where" " " alpha and beta` are complex cube roots of unity, show that,
`xyz = a^(3)+b^(3).`

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CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(SHORT ANSWER TYPE QUESTION )
  1. Find the square roots : y+sqrt(y^(2)-x^(2)) (x6^(2)gt y^(2))

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  2. Find the square roots : a^(2)+(1)/(a^(2))+4i(a+(1)/(a))-2

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  3. If xsqrt2=1+sqrt-1, "find the value of " x^(6)+x^(4)+x^(2)+2.

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  4. Show that one value of (sqrti+sqrt-i)is sqrt2.

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  5. Prove that one value of (1+i)^(1//2)-(1-i)^(1//2)is isqrt2(sqrt2-1).

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  6. Show that one value of (4+3i)^(-1//2)+(4-3i)^(-1//2) is (3sqrt2)/(5).

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  7. If omega be an imaginary cube root of unity, show that, (1-omega)(1-...

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  8. If omega be an imaginary cube root of unity, show that (1+omega-omega...

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  9. If omega be an imaginary cube root of unity, show that (3+3omega+5omeg...

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  10. If omega be an imaginary cube root of unity, show that (xomega^(2)+yom...

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  11. If omega be an imaginary cube root of unity, show that (x+yomega+zomeg...

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  12. If alpha=(-1-sqrt-3)/(2) and beta=(-1+sqrt(-3))/(2), "show that" al...

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  13. Show that , ((-1+sqrt(-3))/(2))^(19)+((-1-sqrt(-3))/(2))^(19)=-1.

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  14. If alpha and beta are the complex cube roots of 1 show that, alpha^(4)...

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  15. Find the value of sqrt([-3+sqrt(({-3+sqrt(-3+... "to infinity"}})]])

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  16. If omega be a complex cube root of unity and x=alpha+beta,y=alpha+beta...

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  17. If x=a+b, y= a alpha+b beta and z=a beta+balpha" "where" " " alpha and...

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  18. If z=x+iy and |z-1|^(2)+|z+1|^(2)=4, determine the position of the poi...

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  19. Factorise : a^(2)-ab+b^(2)

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  20. Factorise : x^(3)+y^(3)

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