Show that the equation ${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-8z+8=0$ has a root of the form \(k\mathrm{

Question

Show that the equation ${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-8z+8=0$ has a root of the form $k\mathrm{i}$, where $k$ is real.[3] Hence solve the equation ${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-8z+8=0$.[3]

Accepted Answer

${2\mathrm{i}}$, ${-2\mathrm{i}}$, ${1+\mathrm{i}}$ and ${1-\mathrm{i}}$

N2006 P1 Q6

N2006 P1 Q6

Video Solution:

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