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To have the courage to think outside the square, we need to be intrigued by a problem. Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries in complex numbers. The first part of Complex Numbers and Vectors provides teachers with background material, ideas and teaching approaches to complex numbers; 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); the specification of curves and regions in the complex plane; and simple transformations of the complex plane. The second part of this resource provides an introduction to vectors and vector spaces, including matrix representation; covers vectors in two- and three-dimensions; their application to specification of curves; 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.