# Complex Analysis

By : Vandana Tanwar

Updated : Jan 28, 2021, 8:46

Complex analysis is that branch of mathematical analysis where complex number functions are investigated. Students preparing for GATE must always be aware of important complex analysis topics for GATE ECE. In mathematical topics, conceptual understanding is required, so while you are preparing for GATE, gather all the complex analysis study material for GATE ECE. To remember the complex analysis formula, you have to practice a lot. While preparing for the GATE exam, you can appear in complex analysis online tests on various online exam preparation platforms.

## Important Complex Analysis Topics

Here are the important topics for GATE ECE.

 Topics Explanation Complex-valued function A complex-valued function is a function such as f: S→Cf:S→C . Here, co-domain is the set of complex numbers CC. Analytic function In Analytic functions, there are convergent power series functions. Holomorphic function In the Holomorphic function, there are one or more complex variables, and in every point of the domain, complexes can be differentiable in some near point. Cauchy–Riemann equations Cauchy–Riemann equations are necessary for the mathematical field of complex analysis. The name Cauchy–Riemann came after Augustin Cauchy and Bernhard Riemann. Cauchy–Riemann equation is a system of two differential equations with differentiability criteria and certain continuity with sufficient complex condition. Formal power series The generalization of a polynomial is known as formal power series in Mathematics. In formal power series terms, numbers are allowed to be infinite, and there is no convergence requirement.

### Tips to Solve Complex Analysis Questions for GATE

• Do regular practice of all the complex analysis formulas a few weeks before the exam.
• Appear in complex analysis online quiz to clear all confusion regarding the concept.
• Follow a definite schedule of practising complex analysis quizzes and stick to it.
• Allot some time from your regular schedule to solving complex analysis MCQ questions.

Importance of Complex Analysis GATE Syllabus in Exams

• Questions from complex analysis asked in GATE exam are critical as it constitutes around 15 to 20 marks.
• Complex analysis GATE questions are not so difficult. With adequate practice, one can score high marks on this part.
• In the GATE exam, complex analysis questions are helpful in Physics also along with Mathematics.
• Complex analysis for computer science students is helpful in the GATE exam to solve mathematical derivations and manipulations.

### Most Recommended Complex Analysis Books

For preparing complex analysis notes for ECE, students must buy a few recommended complex analysis books. Students will get details of the complex analysis GATE syllabus in these books and can start their preparation accordingly.

 Book Author Complex Analysis Jerry R. Muir, Jr. Complex Analysis S.G. Venkatachalapathy Complex Analysis Kevin Houston Complex Analysis Joseph BakDonald J. Newman

## Why Prepare Complex Analysis from BYJU'S Exam Prep?

You can start your GATE preparation from Gradeup, India’s largest online competitive and entrance exam preparation website to get complex analysis GATE notes. You will get all the complex analysis GATE questions and answers PDF on our website. At BYJU'S Exam Prep, we conduct live interactive classes with teachers and faculty members. More than 200 complex analysis MCQ PDFs are available on BYJU'S Exam Prep. Aspiring GATE students can clear the doubts with our faculties regarding the complex analysis syllabus for GATE.

FAQs

Q. Is complex analysis easy or difficult?

Complex analysis is not difficult. Students can learn complex analysis without having a basic knowledge of complex variables.

Q. What is the importance of complex analysis?

Complex analysis has many practical applications as a powerful tool for finding solutions to physical problems.

Q. What is the difference between real and complex analysis?

The real analysis deals with numbers with a one-dimensional number line, while complex analysis deals with two dimensions of the number, imaginary and real, Cartesian style.

Q. When and who discovered complex analysis?

16th-century Italian mathematicians Raphael Bombelli and Girolamo Cardano discovered complex analysis.

Q. Is complex analysis used in Statistics?

No, complex analysis does not have too many uses in Statistics.

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