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

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

If log_(10)(frac{x^3 -y^3}{x^3+y^3}) =2 , then show that dy/dx = (-99x^2)/(101y^2)

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 (x+iy)(3-4i) = 5+12i , then sqrt(x^2+y^2) =

If log_(5) (frac{ x^4 - y^4}{ x^4 + y^4} ) = 2 , show that dy/dx = frac{-12x^3}{13y^3}

Solve the following: If x = 2 cos^(4) (t+3), y= 3 sin^(4) (t+3), then show that dy/dx = - sqrt (frac{3y}{2x})

If log_(10) (frac{ x^3 - y^3}{ x^3 + y^3} ) = 2 , show that dy/dx = frac{-99x^2}{101y^2}

If x/(3x-y-z) =y/(3y-z-x) =z/(3z-x-y) and x+y+z != 0 , then show that the value of each raio is equal to 1.