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Get CBSE Notes for Class 11 Mathematics Chapter 5. Complex Number and Quadratic Equations: Introduction prepared by experts as per the latest NCERT syllabus and CBSE exam pattern. These concise and easy-to-understand notes cover important definitions, formulas, diagrams, and key concepts from the chapter to help students in quick revision and effective exam preparation. Whether you are studying for school tests, board exams, or competitive exams, these notes provide a reliable study resource. Designed in simple language with point-wise explanations, they save time and enhance learning efficiency. Download free PDF notes, explore solved examples, and strengthen your understanding of [Topic Name] for scoring high marks. Perfect for Class 11 students who want clear, structured, and exam-oriented notes for CBSE Mathematics.
First we know about the real number;
π√Real Number includes;
(i) Whole numbers: like 0, 1, 2, 3, 4.................................. etc.
(ii) Rational numbers: like 4/5, 0/6, 0.333........, etc.
(iii) irrational numbers: like π, √3, √2 etc.
We have learnt quadratic equation in previous class. The nature of quadratic equations is
D > 0, {Real and unequal roots}
D = 0, {Real and equal roots}
D < 0, {No Real roots, i.e. Imaginary root}
Look the following example
x2 + 3x + 5 = 0
a = 1, b = 3, c= 5
D =
= 32– 4 ×1 × 5
= 9 – 20
= –11
D < 0, {so equation has no real but imaginary roots}
Now we have to find the roots
Here both the value of x is an imaginary number, which is made by the composition of (i), symbol “i” is called iota. Such number is called complex number.
1. Imaginary Number: A number whose square is negative is known as an imaginary number.
Ex: , , , etc.
2. Complex number: Any number which is of the form of x + iy, where x and y are real number and i = is called a complex number.
Ex : 3 + i5, 2 – i3, 5 + i2 and 4 +i3 etc.
It is denoted by z i.e. z = x +iy, in which Re(z) = x and Im(z) = y
A complex number has two parts;
(I) real part Re(z) {∈ R}
real part : 2, 3, 5, and 4 or may be any real number.
(II) imaginary part Im(z) {Real number with i(iota)}
imaginary part: i, i2, i3, i4, and i5 etc.
Every Real number is a complex number if x∈ R and y ∈ R; such as
z = 3 ⇒ 3 +i0, x = 3, y =0
z = –3⇒ – 3 +i0, x = –3, y =0
z = 7 ⇒ 7 +i0, x = 7, y =0
3. See the following complex numbers
z = 3, z = i3, z = 4, z = i7
z = 3 and z = 4 are purely Real
z = i3 and z = i7 are purely Imaginary
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