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

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

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

If a+ib=(x+iy)/(x-iy) prove that a^2+b^2=1 and b/a=(2xy)/(x^2-y^2)

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

If a +ib = ((x+i)^(2))/(2x-1) then a^(2)+b^(2) is equal to

If x+i y=(a+i b)/(a-i b) prove that x^2+y^2=1

If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)

If y=(cot^(-1)x)^2 , prove that y_2(x^2+1)^2+2x(x^2+1)y_1=2 .

If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)

If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/(4a^2+1) b. ((a+1)^2)/(4a^2+1) c. ((a^2-1)^2)/((4a^2-1)^2) d. none of these