Upto now, we are very much familiar with real numbers. But in solving quadratic equations, real numbers have no answer about -1 i.e, square root of negative numbers. Set of real numbers is a subset of complex numbers. Complex numbers give answers to these questions. This chapter consists of algebraic properties of complex numbers, argand plane , polar representation of complex numbers , fundamental theorem of algebra , Solution of quadratic equations in complex number systems. Square root of a complex number.