Unit-I
D’Moivre’s theorem, application of D’Moivre’s theorem including primitive nth root of unity. Expansions of sin nθ, cos nθ, sinnθ, cosnθ(n∈N). The exponential, logarithmic, direct and inverse circular and hyperbolic functions of a complex variable. Summation of series including Gregory Series.
Unit-II
Hermitian and skew-hermitian matrices, linear dependence of row and column vectors, row rank, column rank and rank of a matrix and their equivalence. Theorems on consistency of a system of linear equations (both homogeneous and non-homogeneous). Eigen-values, eigen-vectors and characteristic equation of a matrix,Cayley-Hamilton theorem and its use in finding inverse of a matrix. Diagonalization.
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Important Questions. (Chapterwise)
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