Write down the real root of ${{w}^{3}}+8=0$, Where $w$ is a complex number. Hence, find the

Question

Write down the real root of ${{w}^{3}}+8=0$, Where $w$ is a complex number. Hence, find the other roots of ${{w}^{3}}+8=0$ in exact form. Deduce the roots of ${{w}^{4}}+{{w}^{3}}+8w+8=0$. Determine the roots of $z$ such that ${{z}^{4}}-\mathbf{i}{{z}^{3}}+8\mathbf{i}z+8=0$.

Accepted Answer

Roots of $w^3+8=0$: $-2$, $1+\sqrt{3}\mathrm{i}$, $1-\sqrt{3}\mathrm{i}$; Roots of $w^4+w^3+8w+8=0$: $-1$, $-2$, $1+\sqrt{3}\mathrm{i}$, $1-\sqrt{3}\mathrm{i}$

2009 NJC P1 Q9 (b) [modified]

2009 NJC P1 Q9 (b) [modified]

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