NCERT Book Class 11 Maths Complex Numbers And Quadratic Equations

5.1 Introduction 

In earlier classes, we have studied linear equations in one and two variables and quadratic equations in one variable. We have seen that the equation x2 + 1 = 0 has no real solution as x2 + 1 = 0 gives x2 = – 1 and square of every real number is non-negative. So, we need to extend the real number system to a larger system so that we can find the solution of the equation x2 = – 1. In fact, the main objective is to solve the equation ax2 + bx + c = 0, where D = b2 – 4ac < 0, which is not possible in the system of real numbers.

5.2 Complex Numbers
Let us denote −1 by the symbol i. Then, we have 2 i = −1 . This means that i is a solution of the equation x2 + 1 = 0. A number of the form a + ib, where a and b are real numbers, is defined to be a complex number. For example,  , are complex numbers.
For the complex number z = a + ib, a is called the real part, denoted by Re z and b is called the imaginary part denoted by Im z of the complex number z. For example, if z = 2 + i5, then Re z = 2 and Im z = 5. Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.

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