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

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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We have .a+i b=((x+i)^(2))/(2 x^(2)+1)=(x^(2)+2 x i+i^(2))/(2 x^(2)+1)=(x^(2)+2 x i-1)/(2 x^(2)+1)=(x^(2)-1)/(2 x^(2)+1)+i (2 x)/(2 x^(2)+1).
.rarr a=(x^(2)-1)/(2 x^(2)+1). and .b=(2 x)/(2 x^(2)+1) a^(2) . x^(2).
.a^(2)+b^(2)=((x^(2)-1)/(2 x^(2)+1))^(2)+((2 x)/(2 x^(2)+1))^(2)=(x^(4)-2 x^(2)+1+4 x^(2))/((2 x^(2)+1)^(2))=(x^(4)+2 x^(2)+1)/((2 x^(2)+1)^(2))=((x^(2)+1)^(2))/((2 x^(2)+1)^(2)).
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V PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
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  2. If (z)(1)=2-i, (z)(2)=1+i, find |((z)(1)+(z)(2)+1)/((z)(1)-(z)(2)+1)|

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  3. 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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  4. Let z1=2-i, z2=-2+i. Find Re((z1z2)/overlinez1)

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

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  6. Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of - 6 ...

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

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

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  9. If alpha and beta are different complex numbers with absbeta = 1, then...

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  10. Find the number of non zero integral solutions of the equation abs(1-i...

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

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

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  13. Show that a real value of 'x' will satisfy the equation (1- ix )/(1+i...

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  14. Find the modulus of the following complex numbers i) 1+i tan alpha i...

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  15. Show that the images of the given complex numbers 3+2 i , 5 i,-3+2 ian...

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  16. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  17. Which of the following is true? i) a)|(z)1+(z)(2)| le|(z)(1)|+|(z)(2)|...

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  18. Represent the complex number z=1+i in the polar form.

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  19. If (5+6 i)/(3+4 i)=x+i y, then find the value of x-y.

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  20. 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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