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If omega ne 1 is a cubic root of unit an...

If `omega ne` 1 is a cubic root of unit and `(1 + omega)^(7)` = A + B`omega`, then (A, B) equals

A

`(1,0)`

B

`(-1,1)`

C

`(0,1)`

D

`(1,1)`

Text Solution

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The correct Answer is:
D
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PREMIERS PUBLISHERS-COMPLEX NUMBERS-Solution to Exercise 2.9
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  3. If |z - (3)/(z)| = 2, then the least value of |z| is

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  4. If |z| = 1, then the value of (1+z)/(1 +bar(z)).

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  5. The solution of the equation |z| -z = 1 + 2i is

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  6. If |z(1)| = 1, |z(2)| = 2, |z(3)| = 3 and |9z(1)z(2) + 4z(1) z(3) + z(...

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  7. If z is a complex number such that z in CC\\RR, and z + (1)/(z) in RR,...

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  8. z(1), z(3), and z(3) are complex numbers such that z(1) + z(2) + z(3)=...

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  9. If (z - 1)/(z + 1) is purely imaginary, then |z| is

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  10. If z = x + iy is a complex number such that |z + 2| = |z - 2|, then th...

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  11. The principal argument of (3)/(-1 + i) is

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  12. The principal argument of (sin 40^(@) + i cos 40^(@))^(5) is

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  13. If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…(1 + n^(2))...

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  14. If omega ne 1 is a cubic root of unit and (1 + omega)^(7) = A + Bomega...

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  15. The principal argument of the complex number ((1 + i sqrt(3))^(2))/(4i...

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  16. If alpha and beta are the roots of x^(2) + x + 1 = 0, then alpha^(2020...

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  17. The product of all four values of (cos"" (pi)/(3) + i sin ""(pi)/(3))^...

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  18. If omega ne 1 is a cubit root unity and |(1,1,1),(1,-omega^(2)-1,omega...

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  19. The value of ((1+sqrt(3)i)/(1 - sqrt(3)i))^(10) is

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  20. If omega = cis (2pi)/(3), then number of distinct roots of |(z+1,omega...

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