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All expansion of the concept of numbers has a suitable realistic elucidation. Complex Number arise quite naturally when you start asking certain basic mathematical questions.This book is an introduction to all popular Complex Number. DeMoivre's Theorem, Functions of Complex Numbers, Logarithm functions, Trigonometric Functions , Hyperbolic Functions,Inverse Trigonometric Functions,Relations between circular and hyperbolic functions is discussed in this book. It is planned for beginners who would like to learn the subject through best practices. We have therefore included a large number of examples along with their theories.It is hoped that the book will be of immense help to graduate and postgraduate students of engineering, science, and computer application. It can be used as a text-cum-reference book by students of BE, BTech, MCA, BCA, M.Sc. and B.Sc. courses.