Class 11 Exercise 1.3 Complex Number | XI Ex 1.3 NEW Maths Federal Board National Book Foundation

Class 11 Exercise 1.3 Unit 1 Complex Number | NEW Maths book Federal Board National Book Foundation

Unit 1 Complex Number
Exercise 1.1
   • Class 11 Exercise 1.1 Complex Number ...  
Exercise 1.2
   • Class 11 Exercise 1.2 Complex Number ...  
Exercise 1.3
   • Class 11 Exercise 1.3 Complex Number ...  
Exercise 1.4
   • Class 11 Exercise 1.4 Q1 Q2 Complex N...  

Unit 2 Matrices and Determinate
Exercise 2.1
   • Class 11 Exercise 2.1 NBF Matrices FB...  
Exercise 2.2
   • Class 11 Exercise 2.2 NBF Matrices FB...  
Exercise 2.3
   • Class 11 Exercise 2.3 NBF Matrices FB...  
Exercise 2.4
Exercise 2.5
Exercise 2.6

Unit 3 vectors
Exercise 3.1
   • Class 11 Exercise 3.1 Vectors NBF | X...  
Exercise 3.2
   • Class 11 Exercise 3.2 Vectors NBF | X...  
Exercise 3.3
Exercise 3.4

Unit 4 Sequence & Series
Exercise 4.1
   • Class 11 Exercise 4.1 Sequence & Seri...  
Exercise 4.2
   • Class 11 Exercise 4.2 Sequence & Seri...  
   • Class 11 Exercise 4.2 Sequence & Seri...  

Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6

Unit 5 Polynomial
Exercise 5.1
   • Class 11 Exercise 5.1 Polynomial NBF|...  
Exercise 5.2
   • Class 11 Exercise 5.2 Polynomial NBF|...  
Exercise 5.3
   • Class 11 Exercise 5.3 Polynomial NBF|...  

Solve the equation with completing square method
Solve the following equation with quadratic formula
Solve simultaneous equation

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Complex numbers are a fundamental concept in mathematics, extending the real number system to include imaginary numbers. They consist of two parts: a real part and an imaginary part.

Definition:

A complex number is a number of the form:

a + bi

where:

a is the real part (a real number)
b is the imaginary part (a real number)
i is the imaginary unit, which satisfies i^2 = -1

Properties:

1. Addition: Complex numbers can be added by adding their real and imaginary parts separately.

(a + bi) + (c + di) = (a + c) + (b + d)i

1. Multiplication: Complex numbers can be multiplied by multiplying their real and imaginary parts, taking into account the fact that i^2 = -1.

(a + bi) × (c + di) = (ac - bd) + (ad + bc)i

1. Conjugate: The conjugate of a complex number a + bi is a - bi, obtained by changing the sign of the imaginary part.

Types of Complex Numbers:

1. Real Numbers: a + 0i (imaginary part is zero)
2. Imaginary Numbers: 0 + bi (real part is zero)
3. Purely Imaginary Numbers: bi (real part is zero, and imaginary part is non-zero)

Applications:

Complex numbers have numerous applications in various fields, including:

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*
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Every year, a large number of students appear for the annual exams conducted by the FBISE. The board's jurisdiction includes ICT, garrisons, northern areas, and other regions in Pakistan.

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