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Complex Numbers (Metric)
Class Details
Tom Baker
Learn, or revise, what complex numbers are, how to do calculations with them, how to use them to solve trig problems, how to define functions on them and how to represent shapes in the plane.
Units
Arithmetic
Addition, subtraction and multiplication; the complex conjugate and its use in division; the Argand diagram. This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.
Modulus and Argument
Complex numbers as vectors with magnitude and direction, and how to do calculations with them. This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.
Why the non-real roots of real polynomials always come in conjugate pairs, and how to use that fact.
The modulus of the product is the product of the moduli; the argument of the product is the sum of the arguments. Similar results for division.
De Moivre's Theorem
Raising complex numbers to powers. Using complex numbers to solve trig problems. \(n\)th roots of complex numbers. This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.
Complex Functions
Functions of complex \(z\). This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.
Loci in the Argand Diagram
Shapes in the plane given by conditions on \(z\). This is a Further Maths topic; Imperial courses that require Further Maths may assume you know it.