## Description

De Moivre’s theorem, application of De Moivre’s theorem including primitive *n*th root of unity. Expansions of sin *n*x, cos *n*x, sin* ^{n}* x, cos

*x. The exponential, logarithmic, direct and inverse circular and hyperbolic functions of a complex variable. Summation of series including Gregory Series.*

^{n}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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