This is termed the algebra of complex numbers. ematics of complex analysis. A number is real when the coefficient of i is zero and is imaginary when the real part is zero. Real analysis provides students with the basic concepts and approaches for internalizing and formulation of mathematical arguments. •Complex dynamics, e.g., the iconic Mandelbrot set. Real analysis with real applications/Kenneth R. Davidson, Allan P. Donsig. Real and Complex Analysis, Integration, Functional Equations and Inequalities by Willi-Hans Steeb International School for Scienti c Computing at University of Johannesburg, South Africa. De•nition 1.2 The sum and product of two complex numbers are de•ned as follows: ! " There is, never­ theless, need for a new edition, partly because of changes in current mathe­ matical terminology, partly because of differences in student preparedness and aims. �gu�wf�*���m=� ��x�ΨI޳��>��;@��(��7yf��-kS��M%��Z�!� }�z�H�{� �d��k�����L9���lU�I�CS�mi��D�w1�˅�OU��Kg�,�� �c�1D[���9��F:�g4c�4ݞV4EYw�mH�8�v�O�a�JZAF���\$;n������~���� �d�d �ͱ?s�z��'}@�JҴ��fտZ��9;��L+4�p���9g����w��Y�@����n�k�"�r#�һF�;�rGB�Ґ �/Ob�� &-^0���% �L���Y��ZlF���Wp ISBN 0-13-041647-9 1. complex number out of two real numbers. I. Donsig, Allan P. II. (If you run across some interesting ones, please let me know!) i{@�4R��>�Ne��S��}�ޠ� 9ܦ"c|l�]��8&��/��"�z .�ے��3Sͮ.��-����eT�� IdE��� ��:���,zu�l볱�����M���ɦ��?�"�UpN�����2OX���� @Y��̈�lc`@(g:Cj��䄆�Q������+���IJ��R�����l!n|.��t�8ui�� Note: The imaginary part of ☞ z =4− 9i is −9 not −9i. This text constitutes a collection of problems for using as an additional learning resource for those who are taking an introductory course in complex analysis.