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Let z=costheta+isintheta. Then the value...

Let `z=costheta+isintheta`. Then the value of `sum_(m->1-15)Img(z^(2m-1))` at `theta=2^@` is:

A

`1/(sin2^(@))`

B

`1/(3sin2^(@))`

C

`1/(2sin2^(@))`

D

`1/(4sin2^(@))`

Text Solution

Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the conjugate of a complex numbers is 1/(i-1), where i=sqrt(-1). Th...

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

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

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

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

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  6. Find the value of 2^4

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

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

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

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  10. The set {R e((2i z)/(1-z^2)): z is a complex number,|z|=1,z=+-1} is.

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  11. The maximum value of |ar g(1/(1-z))| for |z|=1 ,z!=1 is given by

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  12. Find the value of 3^4

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  13. Let alpha and beta be real numbers and z be a complex number. If z^(2...

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  14. If omega is a cube root of unity and (1+omega)^7=A+Bomega then find th...

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  15. Let z be a complex number such that the imaginary part of z is nonz...

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  16. If z ne 1 and (z^(2))/(z-1) is real, then the point represented by the...

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  17. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2+(y-y0)^2...

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  18. What is 3% Equals to

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  19. Express in the form of complex number if z=i^(-39)

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  20. Express in the form of complex number (1-i)^4

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