If `x-iy= sqrt((a-ib)/(c-id))`, prove that `x^(2)+y^(2)=(a^(2)+b^(2))/(c^(2)+d^(2))`.

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

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

If x+iy = (3)/(2+costheta+ isintheta) prove that x^(2)+y^(2)=4x-3

If cos (A /2) =sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

Prove that |(a,b),(c,d)|^(2)=|(a^(2)+c^(2),ab+cd),(ab+cd,b^(2)+d^(2))|

If x,y,a,b,c,d are real and x+iy= sqrt((a+ib)/(c+id))" then "(x^(2)+y^(2))^(2)=

Given (x_(1) + iy_(1)) (x_(2) + iy_(2))…(x_(n) + iy_(n)) = a + ib, show that (x_(1)^(2)+y_(1)^(2))(x_(2)^(2) + y_(2)^(2))(x_(3)^(2) + y_(3)^(2))…(x_(n)^(2) + y_(n)^(2)) = a^(2) + b^(2)

If (x-a)^(2)+(y-b)^(2)=c^(2) , for some c gt 0 , prove that ([1+((dy)/(dx))^(2)]^(3/2))/((d^(2)y)/(dx^(2))) is a constant independent of a and b.

If a,b,c,d are in geometric sequence then prove that (b-c)^(2) +(c-a)^(2) -(d-b)^(2)=(a-d)^2