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If a = cos "" (4pi)/(3) + isin "" (4pi)...

If ` a = cos "" (4pi)/(3) + isin "" (4pi)/(3)` then `((1 + a)/(2))^(3n)` =

A

`((1)/(2))^(3n)`

B

`(- (1)/(2))^(3n)`

C

`( - (1)/(2))^(n)`

D

`((1)/(2))^(n)`

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 (x + y + z...

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  2. 4 + 5 ( - (1)/(2) + (isqrt3)/(2))^(334) + 3 ( - (1)/(2) + (isqrt3)/(2)...

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  3. If a = cos "" (4pi)/(3) + isin "" (4pi)/(3) then ((1 + a)/(2))^(3n) =

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  4. If omega is a cube root of unity , then |{:( 1 , omega , 2 omega^(2)...

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  5. If x^(2) + x + 1 =0 , then the value of (x + (1)/(x))^(2) + (x^(2) + ...

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  6. If 1 , omega , omega^(2) are the cube roots of unity , then the roots...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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