z = x + iy, which satisfies

z^2 + z^ -2 = 8

Find the locus of P in terms of x and y.

Is the general aproach to get a equantion in x and y?

If so, i tried this and ive got z^4 - 8z^2 + 1 = 0

Do i just sub in x + iy as z and expand to get locous?

If not what do i do?