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

If x^2 + y^2 = t + 1/t and x^4 + y^4 = t^2 + 1/t^2 , then show that dy/dx = -1/(x^3y)

IF [log (x^2 + y^2) = 2 tan^-1 (y/x)] then show that , dy/dx = (x+y) /(x- y)

If y = e^(2tan^-1x) , then show that : (1 + x^2)^2 d^2y/dx^2 + 2x ( l +x^2 ) dy/dx= 4y .

If y = e^(2tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 4y

If (x+iy)^(1/3)=a+ib , where a,b,x, y in R, show that x/a-y/b=-2(a^2+b^2) .

If (a+ib)/(c+id)=x + iy , show that : x^2+y^2= (a^2+b^2)/(c^2 +d^2) .

If (1+i)(1+2i)(1+3i)......(1+ni)=(x+iy) , then Show that : 2.5 .10 …… (1+n^(2))=x^(2)+y^(2)

If x,y and z are three real numbers such that x+y+z=4 and x^2+y^2+z^2=6 ,then show that each of x,y and z lie in the closed interval [2/3,2]

If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x-y)