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

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

A

`2^(1//3)cis[(2kpi+pi//3)/(3)],k=0,1,2`

B

`2^(1//5)cis[(2kpi+pi//6)/(3)],k=0,1,2`

C

`2^(1//3)cis[(2kpi-pi//3)/(3)],k=0,1,2`

D

`2^(1//5)cis[(2kpi-pi//6)/(3)],k=0,1,2`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

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

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

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

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

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

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

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

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

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

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  11. If zk=cos((kpi)/(10))+isin((kpi)/(10)) , then z1z2z3z4 is equal to

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  12. The general value of theta which satisfies the equation (costheta+isin...

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  13. sum(k=1)^6[sin((2kpi)/(7))-icos((2kpi)/(7))]=

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  14. The value of prod(k=1)^6((sin)(2pik)/(7)-(icos)(2pik)/(7)) is

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  15. The value of 1+sum(k=0)^14{(cos)((2k+1)pi)/(15)+(isin)((2k+1)pi)/(15...

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  16. If alpha and beta are the roots of the equation x^2-2x+4=0...

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  17. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

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  18. If cosalpha+cosbeta+cosgamma=0=sin alpha+sinbeta+singamma then cos^2al...

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  19. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then cos(2alp...

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  20. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then x^(sin(2...

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