Complex Analysis Notes for Gate 2026
What is Complex Analysis?Complex Analysis is the study of functions defined on complex numbers. Unlike real calculus, complex functions behave more smoothly and have powerful properties that simplify integration and differentiation.
For GATE, this chapter mainly focuses on analytic functions, contour integrals, and series expansions.
The GATE syllabus includes the following topics:
- Analytic Functions
- Cauchy’s Integral Theorem
- Cauchy’s Integral Formula
- Sequences and Series of Complex Numbers
- Convergence Tests
- Taylor and Laurent Series
- Residue Theorem
Most Expected Question Types in GATE
- Checking if a function is analytic/entire.
- Applying Cauchy–Riemann equations.
- Using Cauchy’s Integral Formula to evaluate integrals.
- Convergence radius of power series.
- Taylor/Laurent expansion for simple functions.
- Residue at simple poles, poles of order 2 or 3.
- Contour integral evaluation using residues
- Memorize Cauchy–Riemann equations and their applications.
- Practice at least 20–30 PYQs from GATE Engineering Mathematics.
- Learn to quickly identify singularities and residues.
- Master 10–15 common contour integral patterns.
- Revise Taylor and Laurent expansions regularly.
Download Notes
Conclusion
Complex Analysis is one of the most scoring topics in GATE Engineering Mathematics. With concepts like analytic functions, Cauchy’s theorems, convergence tests, and residue calculus, this chapter helps you solve problems quickly and accurately. A strong hold on these fundamentals ensures you secure guaranteed marks in the GATE exam.Just tell me, Chitti!
