If (a+ib) = `frac{(x+i)^2}{2x^2+1}`, prove that `a^2`+`b^2`= `frac{(x^2+1)^2}{(2x^2+1)^2}`

If a+ib= frac{1+i}{1-i} , then prove that ( a^2 + b^2 )=1

If x+iy= frac{a+ib}{a-ib} , prove that x^2 + y^2 = 1

If x -iy = frac{a-ib}{c-id} , then prove that ( x^2 + y^2 ) = frac{a^2+b^2}{c^2+d^2}

If x-iy = sqrt (frac{a-ib}{c-id}) , prove that (x^2+y^2) = frac{a^2+b^2}{c^2+d^2}

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

If x+iy= sqrt (frac{a+ib}{c+id}) , Prove that, (x^2+y^2)^2 = frac{a^2+b^2}{c^2+d^2}

Integrate the following w.r.t. x: frac{(x-1)^2}{(x^2 + 1)^2}

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

If abs(x) lt 1 , the prove that 2tan^-1x = tan^-1(frac{2x}{1-x^2}) = sin^-1(frac{2x}{1+x^2}) = cos^-1(frac{1-x^2}{1+x^2})

If f(x) = frac {x^2 -1}{x^2 +1} , for every real x, then the minimum value of f(x) is.