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The book is inspired by social media users' exceptional laudation for the author's work
on redeveloping the foundation of complex numbers from the ground up through first
principles. Nowadays complex numbers formed from imaginary numbers have
widespread applications in mathematics, physics and engineering. But many learners
still have difficulties accepting the existence of the imaginary unit because the
property (2) = -1 is used to define while itself is also used to define the property
with remaining undefined despite the abstract representation in the complex plane.
Complex numbers were first introduced so that all polynomials would have solutions.
Traditionally, a top-down approach has been taken in the development of complex
number theory based on (2) = -1. By contrast, the author's work uses a bottom-up
approach in which rotational numbers are introduced to rotate physical vectors through
multiplication. As a result, the re-creation of the imaginary unit, complex numbers and
Euler's formula as well as the discovery of a rotational number set can then be achieved
in the reality without relying on (2) = -1. This removes learners' skepticism about
complex numbers by redefining the imaginary unit as a self-evident presence in daily
life, and makes the complex plane interchangeable with the familiar x-y plane, which
has a direct connection to the real world. The work opens up the opportunity to explore,
extend and share the newly gained comprehensive understanding about complex
numbers for the thorough demystification, popularization and empowerment to broader
educational levels including elementary 6th grade and up.
Like the real number set for 1D (one-dimensional) arithmetic, the existence of the
rotational number set gives rise to 2D arithmetic that greatly simplifies the learning by
allowing elementary students to use the familiar position and rotation concepts of the
physical world without the deep abstract knowledge behind complex numbers. The
contemporary ubiquitous use of touch-screens on mobile phones indicates that selecting
a point on a surface can actually be more primitive and intuitive than selecting a point
on a line, making the 2D arithmetic more appealing. The goal of the book is to provide
an essential read for anyone wanting to keep abreast of the latest understanding of
complex numbers for inspirational learning and teaching.
