Lecture Notes
Main content blocks
- Lecturer: Profile: 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.
Section outline
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I have included further reading in the notes (Section 7) for those who have met complex numbers in depth before, and want to read further, but this material is clearly labelled as being beyond the syllabus.
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