The complex number \(\alpha = a + ib\) is said to be the root (or solution) of a polynomial equation
\[P(z) = a_{n}z^{n} + a_{n-1}z^{n-1} + a_{n-2}z^{n-2} + \dots + a_{0} = 0, \text{ where}\hspace{0.5em} a_{0}, a_{1}, \dots, a_{n} \in \mathbb{C} \text{ if}\]
\[P(\alpha) = 0\]
i.e.,
\[a_{n}\alpha^{n} + a_{n-1}\alpha^{n-1} + a_{n-2}\alpha^{n-2} + \dots + a_{0} = 0.\]

The complex number \(\alpha = a + ib\) is said to be the root (or solution) of a polynomial equation

\[P(z) = a_{n}z^{n} + a_{n-1}z^{n-1} + a_{n-2}z^{n-2} + \dots + a_{0} = 0, \text{ where } a_{0}, a_{1}, \dots, a_{n} \in \mathbb{C} \text{ if}\]

\[a_{n}\alpha^{n} + a_{n-1}\alpha^{n-1} + a_{n-2}\alpha^{n-2} + \dots + a_{0} = 0.\]

Solving Equations involving Complex Numbers

Complex Numbers

International Baccalaureate Higher Level Mathematics

Roots of a polynomial equation

Roots of a polynomial equation