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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: 1. `1/sin2^@` 2. `1/(3sin2^@)` 3. `1/sin2^@` 4. `1/(4sin2^@)`

A

`1//sin2^@`

B

`1//3sin2^@`

C

`1//2sin2^@`

D

`1//4sin2^@`

Text Solution

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The correct Answer is:
D
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MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
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  2. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

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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. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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

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  7. Let omega be the complex number " cos " ( 2pi)/(3) + isin (2pi)/(3)...

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  8. Match the statement in Column I with those in Column II. [Note : He...

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  9. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

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  10. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

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  11. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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

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  13. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  14. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

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

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  16. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

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  17. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

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  18. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

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  19. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  20. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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