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Let z=costheta+isin theta, where i=sqrt(...

Let `z=costheta+isin theta`, where `i=sqrt(-1)`. Then the value of `sum_(m=1)^(15)Im(z^(2m-1))` at `theta=2^(@)` is

A

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

B

`(1) /(3 sin 2^(@))`

C

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

D

`(1)/(4 sin 2^(@))`

Text Solution

Verified by Experts

The correct Answer is:
D
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
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  2. about to only mathematics

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  3. Let z=costheta+isin theta, where i=sqrt(-1). Then the value of sum(m=1...

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  4. If omega is a cube root of unity but not equal to 1, then minimum valu...

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  5. about to only mathematics

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  6. about to only mathematics

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  8. Let a,b in R and a^(2)+b^(2) ne 0. Suppose S={z in C:z=(1)/(a+ibt),t...

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  9. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  10. The quadratic equation p(x)=0 with real coefficients has purely imagin...

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  11. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

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  12. Let a,b,x and y be real numbers such that a-b =1 and y ne 0. If the ...

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  13. If z(1)=p+iq and z(2) = u = iv are complex numbers such that |z(1)|=...

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  14. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

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  15. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

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  17. Find the centre and radius of the circle formed by all the points repr...

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  18. If one of the vertices of the square circumscribing the circle abs(z-1...

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  19. Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...

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  20. If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...

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