Problems and Solutions for Complex Analysis

Got this book to help me prepare for my complex analysis qualifying exam and it did help.

The parent book is *not* one of my favorites in the area of complex analysis. Putting that aside, the author provides accurate solutions (as far as I can tell so far), but it seems like he is reluctant to think like a complex analyst. By that I mean that he often provides inefficient answers by parameterizing complex functions into their real and complex parts when he shouldn't have to. (I remember the section on fractional linear transformations to be a particularly good example of this.)At other times, it seems that he is using his own knowledge instead of what is in the book. (I think I remember him finding radii of convergence by finding the distance from the center to the closest singularity or branch point which I don't think was presented in the section the problems came from.)Anyway, solid choice. You should try to do the problems yourself first, then ask a professor or classmate, and only then should you consult this manual.

This book cannot be used without purchasing the actual book which it represents. This book has some solutions for another complex analysis book. What I thought was, that this book is similar to something like Schaum's solved problems (which is independent and not dependent on another book). In many cases, there is no work shown at all, and simply the answers. So its really of no use and has a deceptive title. I already had 4 other books in complex analysis, so there was no need for me to purchase another book which it represents.

An essential in studying Complex Analysis using Serge Lang's textbook!

I feel some sort of counter balance is in order for the seemingly unbalanced reviews.I have used Lang's UA text and have Shakarchi associated solutions manual. I have found them to be of high quality and are great for self-study or supplemental work. Although I have not yet purchased the Lang / Shakarchi texts on CA, upon online review they appear to be of high quality also.I think it is unfortunate that people feel the need leave such negative reviews for reasons that have little or nothing to do with the text.

I gave a take home test of problems from Lang, because the answers are not in the back of the book. A student challenged my answer to one question, because Shakarchi says the answer is something different. I did not realize anyone had gone to the absurd trouble of publishing answers to the excellent exercises in Lang's book until then. But Shakarchi is wrong, having made a careless error. Reading books of answers to problems is like reading a book about physical exercise only worse, since not only do you not benefit from the exercise of doing it yourself, but you lose most of the potential benefit of the exercise after seeing the answer. At least with physical exercise you do not lose anything from watching it done if afterwards you do it yourself. Look on page 85 of this book where Shakarchi asserts that problems VI.1.26b and VI.1.26e have the same answer because the denominators have the same residues, Well how about the numerators? In 26e the z in the numerator implies that the terms of the laurent series of the quotient are not all of even degree anymore, so I claim (check it! I could be wrong too) the correct answer is that all residues in that case are equal to 2, not zero. (This comes from 2= 1/(1/2) the quotient of the coefficient 1 of the z in the top, and the first non zero coefficient 1/2 of the taylor series of 1-sin at '/2.) So without having read any more of this book, even if this is the only error, I say it is almost worthless to someone really wanting to learn the subject. But if you are like someone who cannot exercise without watching a Jane Fonda video, and you do buy this book, please work the problems yourself, and do not just take the author's word for them. I do recommend Lang's book, and the exercises. Probably my favorite complex book is that by Henri Cartan available in a cheap paperback, and the one by Frederick Greenleaf (available used and in libraries) is excellent for beginners, and he gives the answers (but not the solutions) to most of his exercises right in the book if you want that.