- Lecturer: Andrew Wathen
General Prerequisites:
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.