Complex Numbers

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"A very useful book on complex numbers" - by Vicentiu Radulescu
Mathematics is amazing not only in its power and beauty, but also in the way that it has applications in so many areas. The aim of this book is to stimulate young people to become interested in mathematics, to enthuse, inspire, and challenge them, their parents and their teachers with the wonder, excitement, power, and relevance of mathematics.

This book is a very well written introduction to the fascinating theory of complex numbers and it

contains a fine collection of excellent exercises ranging in difficulty from the fairly easy, if calculational, to the more challenging. As stated

by the authors, the targeted audience is not standard and it "includes high school students and their teachers,

undergraduates, mathematics contestants such as those training for Olympiads or the William Lowell Putnam Mathematical Competition, their coaches, and any person interested in essential mathematics."

The book is mainly devoted to complex numbers and to their wide applications ... full review
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"Five Stars" - by DANT
Excellent for the price
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"Should be a "must read" for math students" - by Carl Mclaren (Haines City, Florida USA)
This inexpensive book covers material not easily found elsewhere but key in understanding complex functions. The problem with complex functions is they are hard to visualize because the input is a plane and the output is another plane. The book covers Circles, Moebius transforms, and Non-Euclidean Geometry. The level is senior undergraduate, 1st year graduate. The book is easy to understand with good exercises. I really like this book.
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"Indispensable" - by Jim Curry (MT)
Complex analysis can challenge the intuition of the new student. This text is unique, among high quality textbooks, in giving a careful and thorough exploration of the geometric meaning underlying the usual algebra and calculus of complex numbers. The Cauchy-Riemann equations define what is meant by a holomorphic function. Restricting to these particularly pleasant and useful functions, the formalism of calculus looks very much like ordinary calculus. Too many students muddle through complex analysis with the notion that it looks like calculus, except some extra nice functions also hold. Such students commonly become competent, but they seldom actually get good at complex analysis. In particular, for many engineers, complex calculus remains an unpalatable mystery, even though they know how to do the calculations. That is the difficulty, and Needham corrects the whole of the difficulty perfectly.

Ahlfors is a great classical text. Conway ... full review
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"A learning how-to for any discipline" - by Robert E. Harvey
An excellent book that is about far more than learning mathematics. The concepts presented are applicable to a wide range of disciplines. I have found it exceptionally useful in the study of music.
"Four Stars" - by Alwyn E. Goodloe (Philadelphia, Pa United States)
This is a wonderful little book much of it accessible to high school students.
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"Very good book. It teaches me all aspects of complex ..." - by Bernhard Metz
Very good book. It teaches me all aspects of complex numbers I need to learn for my study of differential equations, I like the large amount of problems and the solutions. I would find it better if there were all solution in the book not just 50%. The author also took care to show the applications sometimes for example in chapter 5 the visualization of what the line integrals mean is a bit weak. I can recommend this book for someone who wants to have a good overview over complex numbers their applications and properties.
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"One of my main complaints about technical books is ..." - by sp
that they are too verbose, too much geared toward teaching everything to everyone (rather than teaching the basics to everyone), too heavy, and too expensive.

This little slim volume is in some sense an optimal solution to this problem. It covers the very basics of complex analysis in such a way that a typical engineering student
could read the book cover to cover in a short time and come away with a basic understanding of the field. The reader would then be empowered to read up on more specialized topics (e.g., the use of phasors, nyquist stabilty criterion, inverse laplace transforms)
or to apply the theory in an engineering class.

For comparison, I usually tell others that my favorite textbook on complex variables is the book by Wunsch. Although I still like Wunsch's book it has gotten fatter and thicker as it has morphed into
the current third edition. Its sheer bulk ... full review
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"Good book. He is adept with the material" - by Amazon Customer
Good book. He is adept with the material. I also have several other of his Kindle books. Nice refresher for someone needing to review or introduction for someone requiring knowledge of the basics of Complex numbers. Some of his longer proofs may be a bit difficult for a beginner to follow, mainly a matter of style not of subject complexity; it is written by a non mathematician.
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"Exciting introduction to complex variables" - by Jeffrey L. Cooper (North Central Massachusetts, USA)
This book will introduce you to complex numbers, complex variables, and complex functions and you _will_ be able to make the journey. You'll need a little familiarity with algebra but, like all these modern mathematical expositories, you can completely grasp the subject with diligence. The hard or clever parts are spelled out for you.
Perhaps there are some typos but I wasn't hampered appreciably by them. Some beautiful and elegant mathematics is exposed very sensitively in this book and with a great appreciation for the chronology and history of the process. The demonstration bears out Hadamard's comment, "The shortest distance two points in the real plane oftens passes through the complex plane."
This book really spurred on my interest in complex variables. The continued study of complex math can take you to some stunning and unexpected connections in mathematics. I encourage interested readers to consider this ... full review
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"Good reading quality on tablets and PCs" - by Nirasha T.
Since one reviewer complained about readability, I just wanted to say that the quality is really good on my iPad and PC. This book has a fixed layout just like any PDF you will read, so I wouldn't read it on a phone.

Tip: Press "Send a free sample" button on this page before you buy so that you can see how it looks on your device.
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"Getting started in math analysis" - by Palle E T Jorgensen (Iowa City, Iowa United States)
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.

Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some ... full review
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"Exact copy as international edition!" - by ciprian
Same copy as international edition required for most classes!