1. Representation of Complex Numbers and Euler's Formula

2. de Moivere's Theorem and Operations on Complex Numbers

3.  Properties of Complex Numbers nth Root of Unity Complex Power and Logarithm and Hyperbolic Function

4. Complex Function Comples Differentiation Analytic Function Cauchy-Reimann Relations

5. Cauchy-Reimann Relations Corollaries Examples of Analytic Function i. Polynomials

6. Examples of Analytic Functions ii. Exponential Functions iii. Trigonometric Functions iv. Hyperbolic Functions v. Logarithm Functions Cauchy-Reimann Relations in Polar Coordinates 

7. Zeros of Complex Function, Simple Zero, Order of Zeros in Bengali 

8. Singularity, Poles, Essential and Removable Singularity, Branch Points and Branch Cuts 

9. Complex Integration, Examples, Darboux Inequality

10. Cauchy’s Theorem, Corollaries of Cauchy’s Theorem and Morera’s Theorem 

11. Cauchy’s Integral Formula and Extension of Cauchy’s Integral Formula 

12. Generalization of Cauchy's Integral Formula, Cauchy Inequality, Simply Connected and Multiply Connected Regions 

13. Power Series of Complex Function, Taylor Series and Identity Theorem 

14. Laurent Series for Complex Functions having Singularity and Concept of Residue 

15. Residues and Residue Theorem 

16. Applications of Residue Theorem for (i) Integrals with Sinusoidal Functions 

17. Applications of Residue Theorem for (ii) Some Infinite Integrals 

18. Applications of Residue Theorem for (iii) Integrals with Complex Exponential 

19. Applications of Residue Theorem for (iv) Integrals of Multi valued Functions