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.
This course aims to give all students a common background in complex numbers.
Dr Vicky Neale
Students will be able to:
(i) manipulate complex numbers with confidence;
(ii) understand geometrically their representation on the Argand diagram, including the nth roots of unity;
(iii) know the polar representation form and be able to apply it.
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.