2021 ASRJC P1 Q1
Do not use a calculator in answering this question.
It is given that $\text{f}\left( z \right)={{z}^{4}}+2\sqrt{2}{{z}^{3}}+{{z}^{2}}+8\sqrt{2}z-12$. One of the roots of the equation $\text{f}\left( z \right)=0$ is given by $2\mathbf{i}$. By factorising $\text{f}\left( z \right)$ as a product of two quadratic factors, obtain the other roots of the equation.
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