But what is 𝘪, exactly? Demystifying complex numbers, exponential functions and more

Abstract

But What is i, Exactly? tackles the questions that are not dealt with in the high school mathematics curriculum in a simple and approachable, yet detailed and precise manner. Such questions include: What are complex numbers? Why did people, at some point in history, decide to provide solutions for quadratics which previously did not have any? And what is i, exactly? What is the exponential function? Why is it the number e raised to the power of x? Why e, and not some other number? What is e to the power of ix? How does pi emerge from this function? How do we know that pi is an irrational number? Why do we use radians? What does x to the power of y mean when y is an irrational number, like the square root of 2? What about when it is a complex number? And what is 0 to the power of 0? Why is the cube root of -1 equal to -1 on some calculators, yet on more sophisticated calculators, it is equal to some weird complex number? This book is ideal for students who are currently pursuing, or intend to pursue, a mathematics undergraduate course, giving them a sound understanding of what they have learnt in their high school mathematics. It is also a great reference book for mathematics educators teaching at high school or early undergraduate level to supplement their teaching with material that their curriculum overlooks.