2021 ASRJC P1 Q1

Do not use a calculator in answering this question.

It is given that \(\mathrm{f}\left( z \right)={{z}^{4}}+2\sqrt{2}{{z}^{3}}+{{z}^{2}}+8\sqrt{2}z-12\). One of the roots of the equation \(\mathrm{f}\left( z \right)=0\) is given by \(2\mathbf{i}\). By factorising \(\mathrm{f}\left( z \right)\) as a product of two quadratic factors, obtain the other roots of the equation.[4]