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:
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 $\omega^5+1=0$
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
Best Answer
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...]