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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)/(sin 2^(@))`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • Let z = cos theta + isin theta . 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^(@))`

  • If z+(1)/(z)=2costheta , then the value of |(z^(2n)-1)//(z^(2n)+1)|

    A
    `|tan ntheta|`
    B
    `tan ntheta`
    C
    `|cotntheta|`
    D
    `cotntheta`

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    Re{(1+costheta+2iSintheta)^-1}=4 then find theta

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