if `(x+iy)^(1//3)=a+ib`,show that `x/a+y/b=4(a^2-b^2)`

If f(x)=(2x+1)/(3x-2)=y ,show that x=f(y).

if y = sin^-1x , show that (1-x^2) y_2 = xy_1

If (a+ib)(c+id)=x+iy ,prove that x^2+y^2=(a^2+b^2)(c^2+d^2)

If a,b, x in R and (1-ix)/(1+ix)=a+ib ,then prove that a^2+b^2=1

If a,b, xin R and if (1-ix)/(1+ix)=a-ib ,prove that a^2 + b^2 = 1 .

If y=sqrt(x)+(1)/sqrt(x) , then show that 2x(dy)/(dx)+y=2sqrt(x) .

If x + y + z =xyz,show that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2).(2y)/(1-y^2).(2z)/(1-z^2)

If y = tan^(-1)x show that (1+x^2)(d^2y)/(dx^2) + 2x(dy)/(dx) = 0