{"product_id":"discovering-imaginary-numbers-in-everyday-life-the-popularization-of-complex-numbers-hardcover","title":"Discovering Imaginary Numbers in Everyday Life: The Popularization of Complex Numbers - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eQiujiang Lu\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book is inspired by social media users' exceptional laudation for the author's work\u003c\/p\u003e\u003cp\u003eon redeveloping the foundation of complex numbers from the ground up through first\u003c\/p\u003e\u003cp\u003eprinciples. Nowadays complex numbers formed from imaginary numbers have\u003c\/p\u003e\u003cp\u003ewidespread applications in mathematics, physics and engineering. But many learners\u003c\/p\u003e\u003cp\u003estill have difficulties accepting the existence of the imaginary unit  because the\u003c\/p\u003e\u003cp\u003eproperty   = -1 is used to define  while  itself is also used to define the property\u003c\/p\u003e\u003cp\u003ewith  remaining undefined despite the abstract representation in the complex plane.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eComplex numbers were first introduced so that all polynomials would have solutions.\u003c\/p\u003e\u003cp\u003eTraditionally, a top-down approach has been taken in the development of complex\u003c\/p\u003e\u003cp\u003enumber theory based on   = -1. By contrast, the author's work uses a bottom-up\u003c\/p\u003e\u003cp\u003eapproach in which rotational numbers are introduced to rotate physical vectors through\u003c\/p\u003e\u003cp\u003emultiplication. As a result, the re-creation of the imaginary unit, complex numbers and\u003c\/p\u003e\u003cp\u003eEuler's formula as well as the discovery of a rotational number set can then be achieved\u003c\/p\u003e\u003cp\u003ein the reality without relying on   = -1. This removes learners' skepticism about\u003c\/p\u003e\u003cp\u003ecomplex numbers by redefining the imaginary unit as a self-evident presence in daily\u003c\/p\u003e\u003cp\u003elife, and makes the complex plane interchangeable with the familiar x-y plane, which\u003c\/p\u003e\u003cp\u003ehas a direct connection to the real world. The work opens up the opportunity to explore, \u003c\/p\u003e\u003cp\u003eextend and share the newly gained comprehensive understanding about complex\u003c\/p\u003e\u003cp\u003enumbers for the thorough demystification, popularization and empowerment to broader\u003c\/p\u003e\u003cp\u003eeducational levels including elementary 6th grade and up.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eLike the real number set for 1D (one-dimensional) arithmetic, the existence of the\u003c\/p\u003e\u003cp\u003erotational number set gives rise to 2D arithmetic that greatly simplifies the learning by\u003c\/p\u003e\u003cp\u003eallowing elementary students to use the familiar position and rotation concepts of the\u003c\/p\u003e\u003cp\u003ephysical world without the deep abstract knowledge behind complex numbers. The\u003c\/p\u003e\u003cp\u003econtemporary ubiquitous use of touch-screens on mobile phones indicates that selecting\u003c\/p\u003e\u003cp\u003ea point on a surface can actually be more primitive and intuitive than selecting a point\u003c\/p\u003e\u003cp\u003eon a line, making the 2D arithmetic more appealing. The goal of the book is to provide\u003c\/p\u003e\u003cp\u003ean essential read for anyone wanting to keep abreast of the latest understanding of\u003c\/p\u003e\u003cp\u003ecomplex numbers for inspirational learning and teaching.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 192\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.56 x 9 x 6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 08, 2025\u003c\/div\u003e\n            ","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":43155097387071,"sku":"9798992754322","price":51.78,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/iO8zhiSIa-9798992754322.webp?v=1776962174","url":"https:\/\/dhlswag.com\/products\/discovering-imaginary-numbers-in-everyday-life-the-popularization-of-complex-numbers-hardcover","provider":"BBB","version":"1.0","type":"link"}