Complex analysis anu

1. The Origins of Complex Analysis In 1837, nearly three centuries after Cardano's use of 'imaginary numbers', William Rowan Hamilton published the definition of complex numbers as ordered pairs of real numbers subject to certain explicit rules of manipulation

Should I study complex analysis?

Complex analysis is an important component of the mathematical landscape, unifying many topics from the standard undergraduate curriculum.
It can serve as an effective capstone course for the mathematics major and as a stepping stone to independent research or to the pursuit of higher mathematics in graduate school..

What are the objectives of complex analysis?

To study the techniques of complex variables and functions together with their derivatives, Contour integration and transformations.
To study complex power series, classification of singularities, calculus of residues and its applicationsin the evaluation of integrals, and other concepts and properties..

What is a region in complex analysis?

Standard definitions in geometric complex analysis are as follows: A domain is a nonempty open connected set (just as in analysis in general).
A region is a set whose interior is a domain and which is contained in the closure of its interior..