Synopsis
Research Paper (postgraduate) from the year 2017 in the subject Mathematics - Miscellaneous, grade: -, University of Delhi (Shivaji College, University of Delhi, Raja Garden, Delhi), language: English, abstract: Dare to question the very fabric of mathematics? Prepare to have your understanding of numbers challenged in this exploration of the elusive imaginary unit, 'i'. This groundbreaking work delves into the perplexing world of complex numbers, venturing beyond Euler's initial definition to unearth hidden paradoxes and unresolved questions. Journey into the heart of mathematical philosophy as we dissect the relationship between real and imaginary realms, confronting the limitations of current theory. Through rigorous analysis and thought-provoking discussion, this study scrutinizes the properties of 'i', examining its geometric representation and challenging conventional inequalities. Uncover contradictions arising from attempts to compare real and imaginary values, revealing the inherent complexities that lie beneath the surface. Building upon the latest research, including investigations into the convergence of imaginary numbers with infinity, this exploration fearlessly tackles the ambiguities surrounding the sign of 'i' and its implications. Theorems are presented, dissected, and ultimately tested against the bizarre nature of 'i'. Discover how seemingly innocent comparisons between real and imaginary numbers lead to logical impossibilities, forcing a re-evaluation of fundamental mathematical principles. This investigation isn't just an academic exercise; it's a call to action, culminating in the proposal of an open problem designed to ignite future research and push the boundaries of mathematical knowledge. Explore the fascinating world of complex numbers, imaginary units, and the inherent paradoxes that challenge our understanding of real numbers, infinity, and mathematical philosophy; this is a journey into the unknown, where the only certainty is the pres
About the Author
Dharmendra Kumar Yadav got schooling from Putki High School, Putki, Dhanbad. He graduated with Honors from RSP College, Jharia and Post-graduated from P K Roy Memorial College, Dhanbad in Mathematics. He did M. Phil. from Alagappa University, Tamil Nadu. Then he got his doctorate degree from Vinoba Bhave University, Hazaribag, Jharkhand under the supervision of Dr. D. K. Sen on the topic entitled A Study of Indefinite Non-integrable Functions. In Vedic Mathematics He developed Aanuruppen-Binomial Method using Vedic Mathematics formula Aanuruppen Viddhi and Binomial theorem. In Complex Analysis he applied Law of Trichotomy on Imaginary Unit 'iota' and proved many properties related to it. By using it, he extended the real number to Imaginary Number Line and then ended to a Circular Number Line. He proved the Big-bang Theory and Pulsating Theory of the universe by applying the concept of Imaginary unit 'iota'. He has published more than 25 research papers in journals of national & international repute and presented them in more than 10 conferences and seminars. His areas of research are Integral Calculus, Nonelementary Functions, Imaginary Unit, Vedic Mathematics.
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