<ol class="i-list"><li><div class="list-item-paragraph">It is given that&nbsp;$1+a\,\mathbf{i}$ is one of the roots of the equation ${{w}^{3}}+8=0$, where&nbsp;$a$ is a positive constant. 	Without using a calculator, find $a$ and the other roots. <span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Deduce the roots of ${{w}^{4}}+{{w}^{3}}+8w+8=0$. 	<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Hence determine the roots of the equation ${{z}^{4}}-\mathbf{i}\,{{z}^{3}}+8\mathbf{i}\,z+8=0$. 	<span class="inline-marks">[2]</span></div></li></ol>

It is given that $1+a\,\mathbf{i}$ is one of the roots of the equation ${{w}^{3}}+8=0$, where $a$ is a positive constant. 	Without using a calculator, find $a$ and the other roots. 

Deduce the roots of ${{w}^{4}}+{{w}^{3}}+8w+8=0$. 	

Hence determine the roots of the equation ${{z}^{4}}-\mathbf{i}\,{{z}^{3}}+8\mathbf{i}\,z+8=0$. 	

2024 MI PRU2 P1 Q7

2024 MI PRU2 P1 Q7