If (x+yi)^3 = x+yi , find the real values of x and y.

Full solution pls,thanks

(x+yi)^3 = x+yi
(x+yi)^3 - (x+yi) = 0
Let x+yi = z
z^3 - z = 0
z(z^2 - 1) = 0
z(z - 1)(z + 1) = 0
z = 0, z = 1, z = -1

So,
For z=0, x=0, y=0
For z=1, x=1, y=0
For z=-1, x=-1, y=0

x^3+y^3i^3+3xyi(x+yi)=x^3-3xy^2+(3x^2y-y… real x=x^3-3xy^2 img y=3x^2y-y^3