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

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

If (a + 3i) / (2 + ib) = 1 - i, show that 5a - 7b = 0.

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

If (x+iy)^3 = y+vi, then show that y/x+v/y=4( x^2 - y^2 )

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

If y^2 = a^2 cos^2 x + b^2 sin^2 x, show that y + (d^2 y)/(dx^2) = (a^2 b^2)/ (y^3)

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

If x= a cos theta , y= b sin theta , show that ( d^2 y)/(d x^2 ) = - b^4 /a^2y^3

If x= a sin t - b cos t, y= a cos t + b sin t , show that (d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)

If (a+ib)(c+id)(e+if)(g+ih) = A+ iB, then show that ( a^2 + b^2 ) ( c^2 + d^2 )( e^2 + f^2 )( g^2 + h^2 )= ( A^2 + B^2 )