**Dennis G. Zill and Patrick D. Shanahan**

Complex analysis is a fascinating field of mathematics that extends the concepts of real numbers to complex numbers, which are numbers of the form a + bi, where “a” and “b” are real numbers, and “i” represents the imaginary unit. It plays a crucial role in various areas of science and engineering, including physics, electrical engineering, and computer science. Zill’s solution for complex analysis offers a structured approach to understanding and solving problems in this field, making it accessible to a wider audience

## Fundamentals of Complex Numbers

Complex numbers form the foundation of complex analysis. Understanding their properties and operations is essential to grasp complex analysis concepts. Key points to note about complex numbers include:

- Complex numbers consist of a real part and an imaginary part.
- The real part represents the horizontal axis on the complex plane, while the imaginary part represents the vertical axis.

**Analytic Functions and Cauchy-Riemann Equations**

Analytic functions are a crucial aspect of complex analysis. These functions have a derivative at every point within their domain. The Cauchy-Riemann equations provide a necessary condition for a function to be analytic. Important points to consider include:

- Analytic functions satisfy the Cauchy-Riemann equations, which express the relationship between the real and imaginary parts of the function.

## Why is complex analysis so beautiful?

There is one characteristic of Complex Analysis that makes it especially beautiful. **Inside of it we can find objects that appear to be very complicated but happen to be relatively simple**. Reciprocally, there are objects that appear to be very simple but are indeed extremely complex

EX# | DOWNLOAD BELOW LINK |

Exercise 1.1 1-20 | PDF |

Exercise 1.1 21-40 | PDF |

Exercise 1.1 43-55 | PDF |

Exercise 1.2 1-12 | PDF |

Exercise 1.2 13-22 | PDF |

Exercise 1.2 23-32 | PDF |

Exercise #1.3 1-12 | PDF |

Exercise #1.3 13-24 | PDF |

Exercise #1.3 25-38 | PDF |

Exercise #1.4 1-16 | PDF |

Exercise #1.4 17-26 | PDF |

Exercise #1.5 1-12 | PDF |

Exercise #1.5 13-18 | PDF |

Exercise #1.5 19-32 | PDF |

Exercise# 2.1 4-26 | PDF |

Exercise#2.6 1-8 | PDF |

Exercise#2.6 18-26 | PDF |

Exercise#2.6 27-34 | PDF |

Exercise#2.6 Q# 35 to 40 | PDF |

Exercise#3.1 1-10 | PDF |

Exercise#3.1 Q# 11 to 20 | PDF |

Exercise# 3.1 Q# 21 to 30 | PDF |

Exercise#3.1 Q#25 to 30 | PDF |

Exercise#3.2Q# 1-8 | PDF |

Exercise#3.2 Q#17 to 22 | PDF |

Exercise#3.2 Q#22 to26 | PDF |

Exercise#3.3Q3 1-8 | PDF |

Exercise#3.3 Q#9 | PDF |

Exercise#3.3 Q#10 | PDF |

Exercise#4.1 1-14 | PDF |

Exercise#4.1 15-20 | PDF |

Exercise#4.1 Q#33 -46 | PDF |

Exercise#4.2 1-12 | PDF |

Exercise#4.2 13-18 | PDF |

Exercise#4.3 1-10 | PDF |

Exercise#4.3 11-20 | PDF |

Exercise#4.3Q# 21-28 | PDF |

Exercise#4.4Q# 1-6 | PDF |