Second complex root
Task number: 2747
The complex polynomial \((1-i)x^2+(3i-5)x+10\) has a root \(3-i\). Find its other root.
Resolution
We multiply the polynomial by \(\frac{\overline{1-i}}{|1-i|^2}=\frac{1+i}{2}\) yielding the polynomial \(x^2-(4+i)x+5+5i\).
We then divide by \(x-(3-i)\) yielding \(x-(1+2i)\).
Result
The remaining root is \(1+2i\).
