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If a + ib = ((x+i)^2)/(2x^2+1), prove th...

If `a + ib = ((x+i)^2)/(2x^2+1)`, prove that `a^2+b^2 =((x^2+1)^2)/((2x^2+1)^2)`.

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PSEB-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-EXERCISE
  1. Reduce (1/(1- 4i)-2/(1+i)) ((3-4i)/(5+i)) to the standard form .

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  2. If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^...

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  3. Convert the following in the polar form: (1+ 7i)/((2- i)^2)

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  4. Convert the following in the polar form: (1+ 3i)/(1-2i)

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  5. Solve the equation given below:- 3x^2 - 4x+20/3=0

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  6. Solve the equation given below:- x^2 -2x+3/2=0

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  7. Solve the equation given below:- 27x^2 -10x + 1 = 0

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  8. Solve the equation given below:- 21x^2-28x+10=0

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  9. If z1= 2 -i, z2= 1+ i, find |(z1+z2+1)/(z1-z2+1)|.

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  10. If a + ib = ((x+i)^2)/(2x^2+1), prove that a^2+b^2 =((x^2+1)^2)/((2x^2...

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  11. Let z1 = 2 -i, z2 = -2 + i. Find Re((z1z2)/barz1)

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  12. Let z1 = 2 -i, z2 = -2 + i. Find Im(1/(z1barz1))

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  13. Find the modulus and argument of the complex number (1+2 i)/(1- 3i)

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  14. Find the real numbers x and v if (x -iy) (3 + 5i) is the conjugate of ...

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  15. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i) .

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  16. If (x + iy)^3 = u + iv, then show that u/x +v/y = 4(x^2 - y^2)

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  17. If alpha and beta are different complex numbers with |beta|=1, then fi...

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  18. Find the number of non-zero integral solutions of the equation |1- i|^...

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  19. If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a^2 +...

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  20. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

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