Lesson Plan, Class XI (Ch-5) | Complex Numbers

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+1

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Board – CBSE	CLASS –XI	SUBJECT- MATHEMATICS
CHAPTER 5  :- Complex Numbers and Quadratic Equations

TOPIC:- Chapter 5 :- Complex Numbers and Quadratic Equations.

DURATION:-  

This chapter is divided into 10 modules and is completed in 15 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

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 polar representation of complex numbers.

• Statement of fundamental theorem of algebra.

• Solution of quadratic equations (with real coefficients).

• Square root of complex number .

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.

S. No.	Topic [Complex Numbers and Quadratic Equations]
1	Introduction of number system, brief discussion about all types of numbers up-to real numbers.
2	Discuss the need of the numbers which are not real. Concept of imaginary numbers.
3	Square root of unity, concept of iota  “ i” with its values with different powers.
4	Definition and introduction of complex numbers with complete explanation of its real and imaginary parts.
5	Algebraic properties of complex numbers, method of addition, subtraction and multiplication of complex number. Multiplicative inverse of the complex numbers.
6	Geometric representation of a complex number and explanation of the Argand plan.
7	Modulus of complex number, and the value of argument in different quadrants with explanation.
8	Method of writing a complex number in polar form  ie in the form     Z = ( rcosθ+ irsinθ).
9	Method of finding the solution of quadratic equations with real coefficients.
10	Method of finding the square root of the complex number.

EXPECTED 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, polar form of complex number, 
• Method of solving the quadratic equations  
• the method of finding the square root of the complex numbers.

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.

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