But What is i, Exactly?

"I consider the author to be an all-round contributor to the field of mathematics, and this book is one of many testaments to this." - Peter Borg, mathematics professor at the University of Malta.

Dr Alexander Farrugia first started answering questions related to mathematics on Quora in the latter half of the twenty-tens, earning him the Quora Top Writer status in 2017 and 2018. He has selected some of his writings, comprising more than 3000 answers, and incorporated them into this book.

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.