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If x = cos alpha + i sin alpha , y = cos...

If `x = cos alpha + i sin alpha , y = cos beta + i sin beta`, prove that `x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta)`.

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FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
  1. Evaluate i^(59)

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  2. Prove that : (1 + i)^(4n) and (1 + i)^(4n + 2) are real and purely ima...

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  3. If x = cos alpha + i sin alpha , y = cos beta + i sin beta, prove that...

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  4. If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c...

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  5. Solve : x^4 + 4 = 0

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  6. If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega, show th...

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  7. ((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

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  8. If ((1 + i)/(1 - i))^(3) - ((1 - i)/(1 + i))^(3) = x + iy then (x, y) ...

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  9. Evaluate i^(60)

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  10. Fill in the blanks of the following : For any two complex numbers z1...

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  11. Multiplicative inverse of 1 + i is ………..

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  12. arg(z) + arg(barz) (z != 0) is ………..

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  13. If |z| = 4 and arg(z) = (5pi)/6, then z = …………..

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  14. If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c...

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  15. If p +iq = (a + ib)/(a - ib) then p^2 + q^2 = …………

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  16. Evaluate i^(78)

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  17. If a =cos alpha - i sin alpha, b= cos beta - i sin beta, c = cos gamma...

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

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  19. The conjugate of i^(13) + i^(14) + i^(15) + i^(16) is …………

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  20. If -i + 2 is one root of the equation ax^2 - bx + c = 0, then the othe...

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