研究入面常用嘅理論、公式同埋方法包括柯西積分定理、柯西積分公式、留數定理、Laurent級數展開等等。複分析嘅應用領域較為廣泛，喺其它數學分支同埋物理學入面都好有用，包括數論、應用數學、流體力學、熱力學同電動力學等等。
Commonly used theories, formulas, and methods in research include Cauchy integral theorem, Cauchy integral formula, retention theorem, Laurent series expansion, and so on. Complex analysis has a wide range of applications and is useful in other branches of mathematics and physics, including number theory, applied mathematics, fluid mechanics, thermodynamics, and electrodynamics.