Synopsis for Introduction to Complex Numbers

This course will run in the first week of Michaelmas Term.

Generally, students should not 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 and notify their tutor.

Overview

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

Learning Outcomes

Students will be able to:

1. manipulate complex numbers with confidence;
2. understand geometrically their representation on the Argand diagram, including the th roots of unity;
3. know the polar representation form and be able to apply it.

Synopsis

Basic arithmetic of complex numbers, the Argand diagram; modulus and argument of a complex number. Statement of the Fundamental Theorem of Algebra. Roots of unity. De Moivre's Theorem. Simple transformations in the complex plane. Polar form , with applications.

1. R. A. Earl, Bridging course material on complex numbers.
2. D. W. Jordan & P Smith, Mathematical Techniques (Oxford University Press, Oxford, 2002), Ch.6.