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

If u=x/y^(2) - y/x^(2) , then

If (cos theta + isin theta)^(2) = x + iy, then show that x^(2) + y^(2) = 1

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 u=(x-y)^(2) , then (del u)/(del x) + (del u)/(del y) is

If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)/(3!)-y^(4)/(4!)+...

If v(x,y,z) = x^(3) + y^(3) + z^(3) + 3xyz , show that (del^(2)v)/(del y del z) = (del^(2)v)/(del z del y)

If U = (x-y) (y-z) (z-x) then show that U_x+U_y+U_z = 0

If u =x ^(3) +2xy^(2) -x ^(2)y show that (del^(2)u)/(delxdely) =(del^(2)u)/(delydelx).