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

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

A

`cos n theta`

B

`sin n theta`

C

`-i sin" "n" "theta`

D

`itan" "n" "theta`

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The correct Answer is:
D
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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))

AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
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  2. If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

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

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  4. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then (x-y)/(x+y)=

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  5. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then x/y-y/x=

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  6. If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)...

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  7. If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then...

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  8. If n is positive integer and (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) cos...

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

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  10. Show that one value of ((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i...

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  11. If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

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  12. If p=cos2 alpha+isin2 alpha,q=cos2beta+isin2beta then sqrt(p//q)-sqrt(...

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  13. The values of (1-sqrt3i)^(1//3) are

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  14. The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is

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  15. Two of the three values of (-1)^(1//3) are cos(pi//3)+isin(pi//3),cos(...

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  16. One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is

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  17. If z+1/z=1 and z be any complex number,then the value of z^(99)+(1)/(z...

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  18. If (sqrt3-i)^n=2^n,b epsilon 1,the set of integers,then n is a multipl...

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  19. If A+B+C=180^@ and cis A=x,cis B=y,cis C=z, them xyz=

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  20. If xn=cos(pi/2^n)+isin(pi/2^n), then x1 x2 x3......infinity

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