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If z=costheta+isintheta, then (z^(2n)-1)...

If `z=costheta+isintheta`, then `(z^(2n)-1)/(z^(2n)+1)`

A

`cosntheta`

B

`sinntheta`

C

`-isintheta`

D

`itanntheta`

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Match the following. {:(Column-I," "Column-II),(I" : "x=costheta+isintheta" then "x^n-(1)/(x^n),"a) "2isin(alpha-beta)),(II" : If " z=costheta+sintheta" then "(z^n-1)/(z^(2n)+1),"b) "2cos(alpha-beta)),(III" : "x=cisalpha","y=cisbeta" then "x/y+y/x=,"c) "itanntheta),(IV " : " x=cisalpha","y=cisbeta" then "x/y-y/x=,"d) "2iSinntheta):}

(1+costheta-isintheta)^(n)

If n is integer and z = cis theta, ( theta ne ( 2n + 1) pi//2) , then show that (z ^(2n) -1)/(z^(2n) +1) = i tan n theta .

If n is an integer and z=cis theta,(theta ne (2n+1)pi/2), then show that (z^(2n)-1)/(z^(2n)+1)=i tan n theta) .

((1+costheta+isintheta)/(1+costheta-isintheta))^(n)

(1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)

If n is an integer and z=-1+isqrt3," then "z^(2n)+2^(n).z^(n)+2^(2n)

Assertion (A) : (Costheta+iSintheta)^(10)+(Costheta-iSintheta)^(10)=2cos10theta Reason (R) : (1+costheta+isintheta)^n+(1+costheta-isintheta)^n= 2^(n+1)cos^n(theta/2)cos((ntheta)/(2))

DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1
  1. If x+(1)/(x)=2costheta" then "x^(10)+(1)/(x^(10))

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  2. If z^(2)+z+1=0 where z is a complex number, then the value of (z+(1)...

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  3. If z=costheta+isintheta, then (z^(2n)-1)/(z^(2n)+1)

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  4. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)

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  5. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)-(y)/(x)

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  6. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x-y)/(x+y)

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  7. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "x^(m).y^(n)+(1)/(x^...

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  8. If p=cos2alpha+isin2alpha,q=cos2beta+isin2beta" then "sqrt(p//q)-sqrt(...

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  9. If x+1/x=2cos alpha,y+1/y=2cos beta, then xy+(1)/(xy)=

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  10. If alphaandbeta are the roots of the equation x^(2)-x+1=0" then "alpha...

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  11. If alphaandbeta are the roots of x^(2)-2x+4=0" then "alpha^(n)+beta^(n...

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  12. If alphaandbeta are the roots of x^(2)-2x+4=0" then "alpha^(n)-beta^(n...

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  13. If alpha,beta are roots of the equation x^(2)-4x+8=0 then for any ninN...

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  14. If alphaandbeta are the roots of x^(2)-2x+4=0, then the value of alpha...

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  15. If x satisfies the equation x^(2)-2xcostheta+1=0, then the value of x^...

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  16. If a=cos4pi//3+isin4pi//3" then "(1+a)^(3n)

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  17. If cosalpha+cosbeta=0=sinalpha+sinbeta" then "cos2alpha+cos2beta

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  18. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma" then "cos3al...

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  19. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma" then "sin3al...

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  20. If cos alpha+cosbeta+cosgamma = 0 = sinalpha + sinbeta + singamma then...

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