Discovering Imaginary Numbers in Everyday Life

<p>The book is inspired by social media users' exceptional laudation for the author's work</p><p>on redeveloping the foundation of complex numbers from the ground up through first</p><p>principles. Nowadays complex numbers formed from imaginary numbers have</p><p>widespread applications in mathematics physics and engineering. But many learners</p><p>still have difficulties accepting the existence of the imaginary unit 𝑖 because the</p><p>property 𝑖² = -1 is used to define 𝑖 while 𝑖 itself is also used to define the property</p><p>with 𝑖 remaining undefined despite the abstract representation in the complex plane.</p><p></p><p></p><p>Complex numbers were first introduced so that all polynomials would have solutions.</p><p>Traditionally a top-down approach has been taken in the development of complex</p><p>number theory based on 𝑖² = -1. By contrast the author's work uses a bottom-up</p><p>approach in which rotational numbers are introduced to rotate physical vectors through</p><p>multiplication. As a result the re-creation of the imaginary unit complex numbers and</p><p>Euler's formula as well as the discovery of a rotational number set can then be achieved</p><p>in the reality without relying on 𝑖² = -1. This removes learners' skepticism about</p><p>complex numbers by redefining the imaginary unit as a self-evident presence in daily</p><p>life and makes the complex plane interchangeable with the familiar x-y plane which</p><p>has a direct connection to the real world. The work opens up the opportunity to explore</p><p>extend and share the newly gained comprehensive understanding about complex</p><p>numbers for the thorough demystification popularization and empowerment to broader</p><p>educational levels including elementary 6th grade and up.</p><p></p><p></p><p>Like the real number set for 1D (one-dimensional) arithmetic the existence of the</p><p>rotational number set gives rise to 2D arithmetic that greatly simplifies the learning by</p><p>allowing elementary students to use the familiar position and rotation concepts of the</p><p>physical world without the deep abstract knowledge behind complex numbers. The</p><p>contemporary ubiquitous use of touch-screens on mobile phones indicates that selecting</p><p>a point on a surface can actually be more primitive and intuitive than selecting a point</p><p>on a line making the 2D arithmetic more appealing. The goal of the book is to provide</p><p>an essential read for anyone wanting to keep abreast of the latest understanding of</p><p>complex numbers for inspirational learning and teaching.</p><p></p>