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Prove that the complex number ((3+2i)/(2...

Prove that the complex number `((3+2i)/(2-3i)) + ((3-2i)/(2+ 3i))` is purely real.

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we have `((3+2i)/(2-3i))+ ((3-2i)/(2+3i))= (3+2i)/(2-3i).(2+3i)/(2+3i)+ (2-3i)/(2-3i)`
`= ((6-6)+i(9+4))/(4-9i^(2))+ ((6-6)+i(-9-4))/(4-9i)`
`((13i)/13)+ ((-13i)/13)=0 =0+0i` , which is purely real.
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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-section-J (Aakash Challengers Qestions)
  1. Prove that the complex number ((3+2i)/(2-3i)) + ((3-2i)/(2+ 3i)) is pu...

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  2. Let n be even postiive integer such that n/2 is odd and let alpha(0)...

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  3. Let z(1),z(2),z(3) be complex numbers, not all real, such that |z(1)|...

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  4. Let z(1),z(2),z(3) be complex numbers, such that (i) |z(1)|=|z(2)...

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  5. find all complex numbers z such that |z -|z+1|| = |z+|z-1||

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  6. Suppose p is a polynomial with complex coefficients and an even degree...

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  7. The point A(1),A(2)…… A(10) are equally distributed on a circle of rad...

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  8. Let a and b be positive real numbers with a^(3) +b^(3) = a -b and k...

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  9. Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x)...

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  10. If alpha and beta are the roots of the equation x^2 + px -1/(2p^2) =...

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  11. If the roots of the quadratic equation x^2 - ax + 2b = 0 are prime num...

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  12. The number of real solutions of the equation root4(97-x) + root4(x) =5...

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  13. If f(x) is a polynomial of degree at least two with integral co-effic...

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  14. p=(x(1)-x(2))^(2) +(x(1)-x(3))^(2) + .......+(x(1)-x(6))^(2) +(x(2)-x(...

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  15. If x,y,z are three real numbers such that x+ y +z =4 and x^(2) + y^(2...

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  16. If unity is double repeated root of px^3+ g(x^2 + x) +r=0, then

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  17. The number of real solutions of the equation 4x^(99) +5x^(98) + 4x^(9...

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