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Find the value of sum(k=1)^10[sin((2pik)...

Find the value of `sum_(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wherei=sqrt(-1).`

A

i

B

1

C

-1

D

`-i`

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS ENGLISH-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If omega = z//[z-(1//3)i] and |omega| = 1, then find the locus of z.

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  2. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

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  3. Find the value of sum(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wher...

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  4. If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...

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  5. A man walks a distance of 3 units from the origin towards the North-...

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  6. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  7. If abs(z+4) le 3, the maximum value of abs(z+1) is

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  8. Let A, B, C be three sets of complex number as defined below: A={z:Img...

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  9. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  10. Express in the form of complex number i^9+i^(19)

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  11. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

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  12. If the conjugate of a complex numbers is 1/(i-1), where i=sqrt(-1). Th...

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  13. Let z = x + iy be a complex number where x and y are integers. Then...

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  14. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1...

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  15. If |z-4/z|=2 then the greatest value of |z| is:

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  16. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

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  17. about to only mathematics

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  18. If alpha and beta are the roots of the equation x^2"-"x""+""1""=""0 , ...

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  19. The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

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  20. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

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