- Lecturer: Andrew Wathen

Course Term: Michaelmas

Course Lecture Information: This course of two lectures will run in the first week of Michaelmas Term.

Course Overview:

Students should not necessarily expect a tutorial to support this short course. Solutions to the problem sheet will be posted on Monday of Week 2 and students are asked to mark their own problems when no tutorial has been offered.

This course aims to give all students a common background in complex numbers.

This course aims to give all students a common background in complex numbers.

Learning Outcomes:

By the end of the course, students will be able to:

(i) manipulate complex numbers with confidence;

(ii) use the Argand diagram representation of complex numbers, including to solve problems involving the nth roots of unity;

(iii) know the polar representation form and be able to apply it in a range of problems.

(i) manipulate complex numbers with confidence;

(ii) use the Argand diagram representation of complex numbers, including to solve problems involving the nth roots of unity;

(iii) know the polar representation form and be able to apply it in a range of problems.

Course Synopsis:

Complex numbers and their arithmetic.

The Argand diagram (complex plane).

Modulus and argument of a complex number.

Simple transformations of the complex plane.

De Moivre's Theorem; roots of unity.

Euler's theorem; polar form \( r \mathrm{e}^{\mathrm{i}\theta} \) of a complex number.

Polynomials and a statement of the Fundamental Theorem of Algebra.

The Argand diagram (complex plane).

Modulus and argument of a complex number.

Simple transformations of the complex plane.

De Moivre's Theorem; roots of unity.

Euler's theorem; polar form \( r \mathrm{e}^{\mathrm{i}\theta} \) of a complex number.

Polynomials and a statement of the Fundamental Theorem of Algebra.