Understand D'Moivre's theorem and its applications. š
Learn exponential, logarithmic, direct, and inverse circular and hyperbolic functions of a complex variable. ā
Explore summation of series, including Gregory Series. š
Know Hermitian and skew-Hermitian matrices, and the linear dependence of row and column vectors. š§®
Understand eigen-values, eigen-vectors, and the characteristic equation of a matrix. āØ
š Instructions
š§āš« For the Paper-Setter
The question paper will consist of three sections: A, B, and C. š
Sections A and B will have four questions each from their respective syllabus sections. š
Section C will contain one compulsory question with eleven short answer-type questions covering the entire syllabus uniformly. šļø
Sections A and B: Each question will carry 10 marks. š¢
Section C: This section will carry a total of 10 marks. āļø
š For the Candidates
Candidates are required to attempt five questions in total. š
Select two questions from each of Sections A and B. šļø
Additionally, candidates must answer the compulsory question from Section C. š
š Syllabus
Section A š¢
D'Moivre's Theorem:
Applications of D'Moivre's theorem, including primitive nth root of unity. Expressions for sinnĪø, cosnĪø, sin(nĪø), and cos(nĪø). āØ
Functions of a Complex Variable:
Exponential, logarithmic, direct, and inverse circular and hyperbolic functions of a complex variable. š
Summation of Series:
Including Gregory Series and related summation techniques. š
Section B š
Matrices:
Hermitian and skew-Hermitian matrices. Linear dependence of row and column vectors, row rank, column rank, and rank of a matrix, and their equivalence. š§®
Linear Equations:
Theorems on the consistency of a system of linear equations (both homogeneous and non-homogeneous). Eigen-values, eigen-vectors, and the characteristic equation of a matrix. āØ
Cayley-Hamilton Theorem:
Applications in finding the inverse of a matrix. Diagonalization of matrices. š¢
š Previous Year Question Papers of Algebra and Trigonometry