Agenda, Semester Week 4

Agenda, Semester Week 4#

Complex Numbers and Polynomials#

This week will continue our study of the complex numbers. In particular, the polar form of a complex number, which uses the complex exponential function, will be crucial for solving complex polynomial equations.

This leads us to the new topic of the week: the polynomials, a particularly important type of function. We will study polynomials of various kinds and some of their key properties. Polynomials are functional expressions that will be useful for describing many types of behaviour, not least within the topic of kinematics in physics. Polynomials will appear in many connections in later courses, and will play a crucial role in later topics of our course as well as in Mathematics 1b.

Key Terms#

Long Day will cover:

  • Polar form and the complex exponential function.

  • Polynomials in one variable.

  • Degree \(\mathrm{deg}\).

  • Polynomial equations and the quadratic solution formula.

  • Roots, real and imaginary.

  • Polynomials with real coefficients.

Short Day will cover:

  • Binomials and the binomial equation.

  • The identity theorem.

Preperation and Syllabus#

Syllabus this week is the rest of Chapter 4 and the first 4 sections of Chapter 5.

  • For Long Day, read Sections 4.4 through 4.6 and Chapter 5 through Section 5.2.

  • For Short Day, read Sections 5.3 and 5.4.

Exercises#

Exercises for Long Day.

Exercises for Short Day.

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