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 \(1+2i\).

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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