We know that some of the quadratic equations have no real solutions. That means, the solution of such equations include complex numbers. Here, we have found the solution of a quadratic equation ax2 + bx + c = 0 where D = b2 – 4ac < 0. The chapter discusses, in detail, about the need for complex numbers, , to be motivated by the inability to solve some of the quadratic equations. The chapter also enables the students to learn about the algebraic properties of complex numbers, argand plane and polar representation of complex numbers. Statement of the fundamental theorem of algebra, solutions of quadratic equations (with real coefficients) in the complex number system and the square root of a complex number are also among the topics discussed in the chapter.