7
$\begingroup$

Its been two weeks since I've joined this site, and I have received wonderful answers to my complex number questions at the shortest time. I am specially very weak in Complex numbers, and I see such great answers that I wish I could see the solutions to the problems like how the users who answered does. Let's get to the question:

I am looking for a good in depth complex number book for my standard, a book that will help me understand this chapter well. I have posted on this post some of the questions that I have had, so that it gives an idea to what standard I am looking for.

I have seen posts looking for complex analysis books, but those books are too advanced level for me.

The basic summary of my complex analysis course:

enter image description here

Questions I have struggled with:

Here are some of the actual problems that I have had, so it gives a very good idea of the types of questions I struggled:

How to express $z^8 − 1$ as the product of two linear factors and three quadratic factors

How to find $\omega^7$ and $\omega^6$ from $\omega^5+1=0$

Why is $t=\frac{1}{2}$ a root for $\tan 4\theta= \frac{4t-4t^3}{1-6t^2+t^4}=\frac{-24}{7}$, where $t=\tan \theta$

How to find the roots of $(w−1)^4 +(w−1)^3 +(w−1)^2 +w=0$

How to find the roots of $(\frac{z-1}{z})^5=1$

No matter even though I understand one question, when I attempt a different to question, it uses a different strategy. So I think I'll be able to look at problems at a better angle, if I have a good book that suits me

$\endgroup$
6
  • 1
    $\begingroup$ Based on the questions you given, "complex analysis" is the wrong keyword. Complex analysis is, roughly, calculus for functions of a complex variable. The questions you've posted are primarily algebra, not analysis. $\endgroup$
    – Christopher A. Wong
    Oct 28, 2014 at 10:35
  • $\begingroup$ @ChristopherA.Wong Algebra? But this is complex numbers. $\endgroup$
    – The Artist
    Oct 28, 2014 at 10:37
  • $\begingroup$ @TheArtist This is still algebra on the complex numbers. You're not using differentiation or integration here at all. $\endgroup$
    – Ian
    Oct 28, 2014 at 11:05
  • $\begingroup$ @Ian oh ok :) sorry. Il edit my question $\endgroup$
    – The Artist
    Oct 28, 2014 at 11:07
  • 1
    $\begingroup$ @GitGud changed to complex numbers (exactly what my syllabus tells) :) $\endgroup$
    – The Artist
    Oct 28, 2014 at 11:16

1 Answer 1

Reset to default
8
$\begingroup$

The book you want is Andreescu and Andrica's Complex Numbers from A to ...Z .
It contains what you require, but no calculus and no complex function theory, just elementary algebra and geometry .
However it contains material on the subject that is included in no other book, old or new, and will lead you to problems posed at the Mathematical Olympiads.
If you read that book completely (which is certainly not compulsory) you will have the moral satisfaction of understanding results that neither your professor nor 95% of the Faculty of Harvard, Berkeley, Stanford and MIT (to cite some random schools) taken together have the slightest idea about (the remaining 5% having read the book...).
Don't believe me? Ask them point-blank to prove that the incircle of a triangle is tangent to the Euler nine point-circle and watch them squirm :-) [Solution: page 114, but shh...]

$\endgroup$
5
  • 1
    $\begingroup$ (+1) WOW IM SO EXCITED READING YOUR ANSWER :D let me check it out :D $\endgroup$
    – The Artist
    Oct 28, 2014 at 13:20
  • 1
    $\begingroup$ Thank you so much, Im going to start reading this :) And your answer ;) it's the best answer (written completely in english) I have seen so far :D $\endgroup$
    – The Artist
    Oct 28, 2014 at 13:44
  • $\begingroup$ Dear Artist, I'm glad you like this great book, but why do you emphasize that my answer is completely in English? $\endgroup$
    – Georges Elencwajg
    Oct 28, 2014 at 15:07
  • $\begingroup$ s Elencwajg , nono I meant you have the best answer I have seen so far, reason was that I can't tell that it's the best because I have seen some brilliant answers by Did which is in mathematics (solutions, numbers,etc) . But I wanted to praise your answer because it was very nicely formed and this really hit me well and now thanks to you Im really into this book. I wanted to tell something more thank just thank you :) $\endgroup$
    – The Artist
    Oct 28, 2014 at 15:10
  • $\begingroup$ Thank you for the kind words, the Artist. $\endgroup$
    – Georges Elencwajg
    Oct 28, 2014 at 15:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.