Lesson Plan, Class XI (Ch-4) | Complex Numbers

LESSON PLAN MATHEMATICS
CLASS - XI
CHapter - 4 : COMPLEX NUMBERS

lesson plan for maths class XI cbse, lesson plans for mathematics teachers,   lesson plan for maths class XI,  lesson plan for maths teacher in B.Ed. Lesson Plan, 

Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+1	CHAPTER	04	SUBJECT	MATHEMATICS
TOPIC	COMPLEX NUMBERS			DURATION : 08 CLASS MEETINGS

PRE- REQUISITE KNOWLEDGE:

Knowledge of Number System Class 10

Knowledge of trigonometry Chapter 3 class 10+1,

Nature of roots of Quadratic Equations.

TEACHING AIDS:

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:  

Lecture method  and Demonstration

LEARNING OBJECTIVES:

• Need of complex number, to be motivated by inability to solve some of the quadratic equations.

• Algebraic properties of complex numbers.

• Argand plan and modulus of complex numbers.

• Statement of fundamental theorem of algebra.

• Solution of quadratic equations (with real coefficients).

LEARNING  OUTCOMES:

• After studying this lesson student should know  

• Different types of numbers, real numbers, imaginary numbers, 

• Complex numbers and the concept of iota with its values with different powers.

• Students should know the algebraic operations on the complex numbers, 

• Modulus and argand plane of a complex number.

• Method of solving the quadratic equations.

RESOURCES

• NCERT Text Book,

• NCERT Exemplar Book of mathematics,

RESOURCE MATERIAL : 

• Worksheets , E-content, Basics and formulas from  (cbsemathematics.com)

KEY WORDS

Complex Number , Real Part (Re z) , Imaginary Part (Im z) , Real Number , Imaginary Number , Pure Imaginary Number , Standard Form (a + ib) , Conjugate of a Complex Number , Modulus (|z|) , Closure Property , Commutative Property , Associative Property , Distributive Property , Argand Plane , Multiplicative Inverse.

LEARNING ACTIVITIES:

INTRODUCTORY ACTIVITY

EXPERIENTIAL ACTIVITY

ART INTEGRATED ACTIVITY

PROCEDURE :

Start the session by asking the questions related to the number system  of 10^th standard and discuss the transformation of trigonometric functions in different quadrants with the students. 

Also recapitulate the concept of converting degree measure into radian measure and the nature of roots of quadratic equations.  

Now introduce the topic complex number and quadratic equations  step by step as follows.

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[COMPLETE EXPLANATION]

Introduction of number system, brief discussion about all types of numbers up-to real numbers.

Real numbers:
All rational and irrational numbers are called real numbers.

Non-Real Numbers :
The numbers which are not real are called non real numbers. These numbers are also called imaginary numbers.

Discuss the need of the numbers which are not real. Concept of imaginary numbers.

Square root of unity, concept of iota “ i” with its values with different powers.

Imaginary numbers :-
Square root of a negative real number is called the imaginary number.

Definition and introduction of complex numbers with complete explanation of its real and imaginary parts.

Complex Number:
All real and non- real numbers are called complex number

OR

A number of the form a + ib is called a complex number. Here a and b are the real numbers and i is called the iota.

For example  Z = a + ib,  where a is called real part and b is called imaginary part. 

 Value of iota is √-1
i = √-1 ,  i² = -1,   i³ = - i,   i⁴ = 1

Geometrical Representation of the values of iota.

Algebraic properties of complex numbers, method of addition, subtraction and multiplication of complex number. Multiplicative inverse of the complex numbers.

Addition of two complex numbers 

Two complex numbers are added by simply adding their real and imaginary parts

If Y = a + ib and Z = c + id then

Y + Z = (a + c) + i(b + d)

Properties of addition of two complex numbers

i) Closure Property:

Addition of two complex numbers holds the closure property. This means that addition of two complex numbers is also a complex number.

ii) Commutative Property:

Addition of complex numbers is commutative. 

⇒ Y + Z = Z + Y

iii) Associative Law:

Addition of complex numbers holds associative law 

⇒ (X + Y) + Z = X + (Y + Z)

iv)Existence of additive identity: 

0 is the additive identity for the addition of complex number.  
∵ Z + 0 = Z

v) Existence of additive inverse : 

If Z is a complex number then - Z is called the additive inverse of Z.      

∵ Z + ( - Z) = 0

Subtraction of two complex numbers : 

Two complex numbers are subtracted by subtracting their corresponding real and imaginary parts. 

If  Y = a + ib,   Z = c + id then

Y - Z = (a + ib) - (c + id)

         = (a - c) + i(b - d)

Multiplication of two complex numbers 

If Y = a + ib,  Z = c + id then  

YZ = (a + ib)(c + id)

      = ac + iad + ibc + i²bd 

      = ac + i(ad + bc) + (-bd)

      = (ac - bd) + i(ad + bc) 

Conjugate of a complex number 

If Z= a+ib is a complex number then conjugate of Z is denoted by  and is given by 
 

Note:- Conjugate of the conjugate of complex number is the complex number itself.

If Z = a + ib, then 

 

Modulus of complex number

If Z = a + ib is a complex number then modulus of Z is denoted by |Z| and is given by   

Geometric representation of a complex number and explanation of the Argand plan.

Argand Plane : 

The plane having a complex number assigned to each of its point is called a complex plan or Argand plane.

Every point of the form (x, y) can be represented in the cartesian coordinate plane.

When a complex number is represented in the plan then the plane is called a complex plane or Argand plane.

In Argand plane x- axis is called real axis and y-axis is called imaginary axis.

If Z = x + iy then 

|Z| is the distance of the point (x, y) from the origin (0, 0)

Let point P represent the complex number Z = x + iy. Let directed line OP = |Z| = r and θ is the angle which OP makes with the positive direction of x - axis. 

STUDENTS DELIVERABLES:

• Review questions given by the teacher. 

• Students should prepare the presentation individually or in groups on the  Argand plan and the representation of the complex number in the polar form.  

• Solve NCERT problems with examples.

EXTENDED LEARNING:

Students can extend their learning in   through the Resource Centre Mathematics . Students can also find many interesting topics on mathematics at the site:   cbsemathematics.com

ASSESSMENT TECHNIQUES:

• Assignment sheet will be given as home work at the end of the topic. 

• Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.

• Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.

• Re-test(s) will be conducted on the basis of the performance of the students in the test.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

• Puzzle

• Quiz

• Misconception check

• Peer check

• Students discussion

• Competency Based Assessment link: M C Q

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