VIC: Taylor Polynomials

Objectives

• Complex numbers in polar form (modulus and argument)
• Proof of basic identities involving modulus and argument
• Proof of DeMoivre’s Theorem for integral powers

Vocabulary

• Taylor Series,
• Taylor Polynomial,
• Complex numbers in rectangular form,
• Complex numbers in polar form
• Modulus
• Argument

About the Lesson

A Taylor polynomial is a finite number of terms from a Taylor series.  In this activity Taylor polynomials are used that approximate exponential and trigonometric functions.  The introduction of the complex number i shows how the trigonometric functions can be added to produce the exponential function and therefore making the link between the two types of polar representation of a complex number.