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If z=(costheta+isintheta), show that z^(...

If `z=(costheta+isintheta)`, show that `z^(n)+(1)//(z^(n))=2cosntheta and `z^(n)-(1)(z^(n))=2isinntheta

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The correct Answer is:
`2isinntheta`
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PREMIERS PUBLISHERS-COMPLEX NUMBERS-Problem for practice
  1. If z=(costheta+isintheta), show that z^(n)+(1)//(z^(n))=2cosntheta and...

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  2. If (1-i)/(1+i) is a root of the equation ax^(2)+bx+1=0. Where a, b...

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  3. If is a cubeth root of unity root of : (1-omega+omega^(2))^(4)+(1+om...

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  4. The arguments of the roots of a complex number differ by :

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  5. If z(1)=4+5i and z(2)=-3+2i that (z(1))/(z(2)) is :

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  6. The number of values of (costheta+isintheta)^(p//q) where p and q are ...

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  7. If -i+3 is a root of x^(2)-6x+k=0. Then the value of k is :

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  8. If x^(2)+y^(2)=1, then the value of (1+x+iy)/(1+x-iy).

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  9. The value of ((-1 + isqrt3)/(2))^(100) + ((-1-isqrt3)/(2))^(100) is :

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  10. The principal value of arg(z) lies in the interval :

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  11. If -barz lies in the third quadrant then z lies in the :

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  12. If P is ((1)/(2)+i(sqrt(3))/(2)) and OP is rotated through an angle (p...

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  13. If the amplitude of a complex number is (pi)/(2) then the number is :

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  14. If A+iB=(a(1)+ib(1))(a(2)+ib(2))(a(3)+ib(3)) then A^(2)+B^(2) is :

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  15. The points z(1)z(2)z(3)z(4) in the complex plane are the vertices of a...

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  16. If omega is the cube root of unity, then then value of (1 - omega) (1 ...

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  17. Find the correct statement : The cube roots of unity are :

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  18. Which of the following is incorrect.?

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  19. Which of the following is incorrect ?

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  20. Which of the following is incorrect ?

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  21. Which of the following is correct statement ?

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