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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:
`2 i sin n theta`
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FULL MARKS-COMPLEX NUMBERS -EXERCISE - 2.9
  1. If z=(costheta+isintheta), show that z^(n)+(1)//(z^(n))=2cosntheta and...

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  2. i^(n) + i^(n+1) + i^(n + 2) + i^(n + 3)

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  3. The value of sum(i=1)^(13) (n^(n) + i^(n-1)) is

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  4. The area of the triangle formed by the complex numbers z, iz, and z + ...

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  5. The conjugate of a complex number is (1)/(i-2). Then, the complex numb...

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  6. If z= ((sqrt(3) + i)^(3) (3i+4)^(2))/((8 + 6i)^(2)), then |z| is equal...

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  7. If z is non zero complex number, such that 2i z^(2) = bar(z),then |z| ...

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  8. If |z-2 + i|le2, then the greatest value of |z| is

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  9. If |z - (3)/(z)| = 2, then the least value of |z| is

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  10. If |z| = 1, then the value of (1+z)/(1 +bar(z)).

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  11. The solution of the equation |z| -z = 1 + 2i is

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  12. If |z(1)| = 1, |z(2)| = 2, |z(3)| = 3 and |9z(1)z(2) + 4z(1) z(3) + z(...

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  13. If z is a complex number such that z in CC\\RR, and z + (1)/(z) in RR,...

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  14. z(1), z(3), and z(3) are complex numbers such that z(1) + z(2) + z(3)=...

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  15. If (z - 1)/(z + 1) is purely imaginary, then |z| is

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  16. If z = x + iy is a complex number such that |z + 2| = |z - 2|, then th...

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  17. The principal argument of (3)/(-1 + i) is

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  18. The principal argument of (sin 40^(@) + i cos 40^(@))^(5) is

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  19. If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…(1 + n^(2))...

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  20. If omega ne 1 is a cubic root of unit and (1 + omega)^(7) = A + Bomega...

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  21. The principal argument of the complex number ((1 + i sqrt(3))^(2))/(4i...

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