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If omega is a complex cube root unity th...

If omega is a complex cube root unity then `sin { (omega^(10) + omega^(23)) pi - (pi)/(4)}` equals

A

`(-sqrt3)/(2)`

B

`(1)/(sqrt2)`

C

`(-1)/(2)`

D

`(sqrt3)/(2)`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If 1 , omega , omega^(2) are the cube roots of unity , then the roots...

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  2. If omega is a complex cube root of unity , then the value of (a + b o...

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  3. If omega is a complex cube root unity then sin { (omega^(10) + omega^(...

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  4. If z + (1)/(z) = -1 then z^(5) + (1)/(z^(5)) =

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  5. If (omega ne1) is a cube root of unity , then {:(1 , 1 + i+ omega^(2...

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  6. If n (ne 3) is an integer and z = -1 + isqrt3 , then z^(2n) + 2^(n) ,...

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  7. If |(z - 4bari)/(z-2)| = 2 then the locus of z is

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  8. The locus of the point z=x+iy satisfying |(z-2i)/(z+2i)|=1 is

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  9. If |z| = sqrt2 then the point given by "3 + 4z" lies on a circle whos...

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  10. The complex equation |z + 1- i| = |z + i-1| represents a

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  11. If z = x + iy is a complex numbers z for which |z +i//2|^(2) = |z - i/...

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  12. If |z + barz| + |z - barz| = 2 then z lies on

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  13. If |z^(2) - 1| = |z|^(2) + 1 , then z lies on

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  14. If omega is a complex cube root of unity , then sum(k = 1)^(6) ( omega...

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  15. If z(barz+3)=2 then the locus of z = x + iy is

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  16. If alpha + ibeta = tan^(-1) (z) , z = x +iy and alpha is constant then...

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  17. If (z - i)/(z +1) is purely imaginary then the locus of z = x +iy is

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  18. If log (tan 30^(@)) ( (2 |z|^(2) + 2 |z| - 3)/(|z| + 1)) lt -2 , then

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  19. The locus of z satisfying the inequality log ((1)/(3)) |z + 1| gt log(...

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  20. If z(1) = 8 + 4i , z(2) = 6 + 4i and z be a complex number such that ...

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