 Ch05. Complex Numbers & Quadratic Equations

Ch05. Complex Numbers & Quadratic Equations

In this self study course, you will learn Need for complex numbers, especially {\displaystyle \sqrt{-1} } , to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers.Argand plane and polar representation of complex numbers. solution of quadratic equations (with real coefficients) in the complex number system.Square root of a complex number. This course also has solutions of NCERT Exercise questions.

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Course Content

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Cartesian and Polar Coordinate Systems

Relationship between Cartesian and Polar Coordinate Systems

Argand Diagram to represent Complex Numbers

Polar Representation of Complex Numbers

Modulus and Argument of Complex Numbers

Questions based on Polar Form, Modulus & Arguments

NCERT Exercise 5.2

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Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Conjugate of Complex Numbers

NCERT Examples

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Example 8

Example 12

Example 14

Example 15

Example 16

Miscellaneous Exercise

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Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 20

Question 19

Question 18

Question 17

Supplementary Exercise

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Square root of Complex Number

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Question – 6

Imaginary Numbers and Complex Numbers

Working with Imaginary Numbers and Complex Numbers

NCERT Exercise 5.1

NCERT Exercise 5.3

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