Module Information

Module Identifier
Module Title
Geometry of Complex Numbers
Academic Year
Semester 1
External Examiners
  • Dr Andrew Hazel (Reader - University of Manchester)
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 22 x 1 Hour Lectures


Assessment Type Assessment length / details Proportion
Semester Assessment Written Solutions  4 problem sheets  20%
Semester Exam 2 Hours   Written Exam  80%
Supplementary Assessment 2 Hours   Written Exam  100%

Learning Outcomes

On successful completion of this module students should be able to:

Identify the properties of complex functions and describe their effects on objects in the complex plane.

Understan the effect of a range of mapping including the exponential, cosine multifunctions and logarithmic functions.

Demonstrate a broad understanding of the properties of Mobius transformations and their applications.

Understand the process of stereographic projection.

Brief description

This course aims to develop the student's grasp of the geometric signficiance of complex transformations and their mapping properties. Students will solve problems with a number of transformations, including Mobius transformations and stereographic projections, which are important in a number of contemporary contexts.


Geometry of complex arithmetic: Euler's theorem revisited, applications, Euclidean geometry.

Complex functions as transformations: the exponential function, the cosine and sine functions, multifunctions and logarithmic functions.

Mobius transformations: Inversion, the Riemann sphere, sterographic projection, Mobius transformations, visualistion and classification, decomposition, automorphism.

The geometry of complex differentiation: Local description of mapps, conformality, physical applications.

Module Skills

Skills Type Skills details
Application of Number
Communication Written answers to questions must be clear and well structured and should communicate stuent's understanding.
Improving own Learning and Performance Students are expected to develop their own approach to time management regarding the completion of Example sheets on time, assimilation of feedback, and preparation between lectures.
Information Technology Use of Blackboard.
Personal Development and Career planning N/A
Problem solving Throughout
Research skills Students will be encouraged to indepenently find and assimilate useful resources.
Subject Specific Skills Students will become accomplished at solving problems in a major area of applied mathematics.
Team work Students will be encouraged to independently find and assimilate useful resources.


This module is at CQFW Level 6