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The modulus of the complex number ((1-is...

The modulus of the complex number `((1-isqrt3)(cos theta+isin theta))/(2(1-i) (cos theta-i sin theta))` is

A

A) `(1)/(sqrt2)`

B

B) `(1)/(2 sqrt2)`

C

C) `(1)/(sqrt3)`

D

D) None of these

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • We express ((cos 2theta -i sin 2theta)^(4) (cos 4theta + i sin 4 theta)^(-5))/((cos 3theta + i sin 3theta)^(-2) (cos 3theta -i sin 3theta)^(-9)) in the form of x+iy , we get

    A
    `cos 49theta-i sin 49 theta`
    B
    `cos 23theta- i sin 23theta`
    C
    `cos 49theta+ i sin 49theta`
    D
    `cos 21theta+ i sin 21theta`

  • (sin3theta)/(2cos2theta+1)=(1)/(2) if

    A
    `theta=2npi+(pi)/(6)`
    B
    `theta=2npi-(pi)/(6)`
    C
    `theta=npi+(-1)^(n)(pi)/(6)`
    D
    `theta=npi-(pi)/(6)`

  • If sintheta,1,cos2theta are in GP ,then theta=

    A
    `npi+(-1)^(n)(pi)/(2)`
    B
    `npi+(-1)^(n-1)(pi)/(2)`
    C
    `2npi`
    D
    None of these

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    The product of matrices A = [(cos^(2) theta, cos theta sin theta),(cos theta sin theta , sin^(2) theta)] and sin B = [(cos^(2)phi, cos phi sin phi),(cos phi sin phi, sin^(2) phi)] is a null matrix if theta - phi =

    int ((sin theta +cos theta ))/(sqrt(sin 2 theta)) d theta is equal to :

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