I am searching for a good book to cover topics of complex numbers. Please refer book on complex numbers - especially covering equations of complex variables topic . Example :
If $\alpha$ is a complex constant such that $\alpha z^2 +z +\overline{\alpha} =0$ has real root then prove that $\alpha +\overline{\alpha} =1$
or any equations in cubic, quadratic etc. in complex form.
I have referred complex numbers from A to Z by Titu Andreescu but it doesn't cover this topic .
I will be greatful to you. Thanks..
"Geometry of Complex Numbers" by Hans Schwerdtfeger ( inexpensive published by dover ) and "Introduction to the Geometry of Numbers" by Roland Deaux ( this one also published by dover ) , Links: http://books.google.com/books/about/Geometry_of_Complex_Numbers.html?id=4XE2_AqxYVkC and http://books.google.com/books/about/Introduction_to_the_Geometry_of_Complex.html?id=PN5UAAAAYAAJ
This second doesn't seem to have much in the way of a preview, perhaps you can check Amazon or Barnes & Noble.