Fundamental Theorem of Algebra

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Fundamental Theorem of Algebra (Jump to: Lecture | Video )

Complex Number
A complex number is any number written in the form: a + bi Where ‘a’ and ‘b’ are real numbers, and ‘i’ is the imaginary unit.

Complex Number

A complex number is any number written in the form:

a + bi

Where ‘a’ and ‘b’ are real numbers, and ‘i’ is the imaginary unit.

Fundamental Theorem of Algebra
Every polynomial equation with complex coordinates and a degree greater than zero has at least one root in the set of complex numbers.

A polynomial equation with degree n will have n roots in the set of complex numbers.

Solve the below polynomial equation, and determine its number of roots:

Figure 1.

This polynomial equation has one (repeating) root.

Descartes’ Rule of Signs can be used to determine the number of positive real zeros, negative real zeros, and imaginary zeros in a polynomial function.

It is the topic of the next lecture.