De-Moivre's Theorem; Important Deductions form De-Moivre's Theorem; Expansions of Some Trigonometrical Functions; Exponential, Trigonometric and Hyperbolic Functions of a Complex Number; Separation Into Real and Imaginary Parts; Logarithms of Complex Numbers; Inverse Circular and Hyperbolic Function of Complex Numbers; Gregory's Series; Summation of Trigonometrical Series; Trigonometrical Expansions; Transformation of Equations; Basic Concepts and Rank of a Matrix; Linear Equations; Inverse of a Matrix; Eigen Values and Eigen Vectors; Elements of Set Theory; Groups; Normal Subgroups; Rings