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if x(k) = cos pi/3^(k) + isin pi/3^(k)...

if ` x_(k) = cos pi/3^(k) + isin pi/3^(k) ` , find ` x_(1)x_(2)x_(3)……oo`
(ii) Express `((1+sin alpha + I sin alpha)/(1 + sin alpha -icos alpha))^(n)` in the form A + B

A

1

B

`-1`

C

i

D

`-i`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. Let g(x) and h(x) are two polynomials such that the polynomial P(x) =g...

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  2. If g(x) and h(x) are two polynomials such that the polynomials P(x)=g(...

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  3. if x(k) = cos pi/3^(k) + isin pi/3^(k) , find x(1)x(2)x(3)……oo (...

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  4. If (a1+ib1)(a2+ib2).....(an+ibn)=A+iB, then (a1^2+b1^2)(a2^2+b2^2).......

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  5. If (a(1)+ib(1))(a(2)+ib(2))………………(a(n)+ib(n))=A+iB, then sum(i=1)^(n) ...

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  6. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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  7. If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...

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  8. prove that tan(i" In"((a-ib)/(a+ib)))=(2ab)/(a^(2)-b^(2)) (where a, ...

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  9. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

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  10. The locus of the points representing the complex numbers z for which |...

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  11. For n=6k, k in z, ((1-isqrt(3))/(2))^(n)+((-1-isqrt(3))/(2))^(n) has t...

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  12. The product of all values of (cosalpha+isinalpha)^(3//5) is

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  13. If C^(2)+S^(2)=1, then (1+C+iS)/(1+C-iS) is equal to

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  14. The centre of a square ABCD is at z=0, A is z(1). Then, the centroid o...

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  15. The number of solutions of the system of equations "Re(z^(2))=0, |z|=2...

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  16. The vector z=-4+5i is turned counter clockwise through an angle of 180...

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  17. The value of [sqrt(2)(cos(56^(@)15^('))+isin(56^(@)15^('))]^(8), is

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  18. Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)...

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  19. The vertices B and D of a parallelogram are 1-2i and 4-2i If the diago...

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  20. If the complex number z(1) " and " z(2) are such that arg (z(1)) - ar...

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