Complex Numbers - Finding Roots of Equations with Complex Coefficients

Complex Numbers - Finding Roots of Equations with Complex Coefficients

Given that \(1+2\mathbf{i}\) is a root of the equation \(z^{3}-4z^{2}+(6+\mathbf{i})z-5+5\mathbf{i}=0\), find the other roots of the equation.

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Answer:\(z=3-\mathbf{i}\ \text{or}\ -\mathbf{i}\)

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