Complex Numbers and Vectors

Complex Numbers and Vectors is an informative resource for advanced mathematics teachers or students undertaking advanced maths courses that draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes and stories from mathematical history to explain the mathematics of vectors and the discoveries in complex numbers.

The title is split into two parts:

• Part 1 provides teachers with background material, ideas and teaching approaches to complex numbers: o Including models for complex numbers and their geometric and algebraic properties, their role in providing completeness with respect to the solution of polynomial equations of a single complex variable (the fundamental theorem of algebra) and the specification of curves and regions in the complex plane; and simple transformations of the complex plane.
• Part 2 provides an introduction to vectors and vector spaces: o Including matrix representation (covers vectors in two- and three-dimensions), their application to specification of curves and vector calculus and their elementary application to geometric proof

Technology has been used throughout the text to construct images of curves, graphs and two and three dimensional shapes.