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Fill in the blanks of the following :
For any two complex numbers `z_1, z_2` and any real number a, b,
`|az_1 - bz_2|^(2) + |bz_1| + az_2|^(2) = …………`

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The correct Answer is:
`(a^2 + b^(2)) (|z_1|^2 + |z_2|^2)`
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FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
  1. ((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

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

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  3. Evaluate i^(60)

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

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

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

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

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

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

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  10. Evaluate i^(78)

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

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

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

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

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  15. The equation having 4 + 3i and 4 - 3i as root is ………..

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  16. If 2−i is one root of the equation ax^2+bx+c=0, and a,b,c are rational...

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

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  18. If omega is a cube root of unity, then the value of (1 - omega + omega...

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

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

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