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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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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Solve the following equation : x^2-(3 sqrt2 -2i)x-6 sqrt2 i=0.

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  2. Solve the following equation : 2x^2-(3 +7i)x + (9i-3)=0.

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  3. Reduce (1/(1- 4i)-2/(1+i)) ((3-4i)/(5+i)) to the standard form .

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

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

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

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

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

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

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  11. Convert z= (i-1)/(cos frac (pi)(3)+i sin frac (pi)(3)) in polar form.

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  12. Find the non-zero integral solutions of |1-i|^x=2^x.

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

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  14. If z1 =-3i, z2= 3 +4i and z3=2- 3i, verify that z1(z2+z3)=z1z2+z1z3.

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  15. 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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  16. If a^2+b^2=1, prove that (1+b+ia)/(1+b-ia)= b + ia.

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

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

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

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

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