Class 11 Math EX 1.2 Q1 to Q4 FBISE & KPK Sir Waqar Hussain

In this online lecture by Syed Waqar Hussain , the focus is on intermediate Part 1 Mathematics science group Chapter 1, complex numbers. The lecture specifically covers Exercise 2.1, with a detailed explanation of Question No. 1 to Question No. 4 all parts. This video lecture provides a comprehensive explanation of Exercise 2.1, covering the entire syllabus approved by the government for 11th-grade Mathematics Science Group. The content is based on the khyber pakhtunlhwa Textbook Board's curriculum and is suitable for students studying in any of the Punjab boards, Federal board, Sindh board, or KPK board. The lecture is available in Urdu, and English languages, making it accessible to a wide range of learners. The content is designed to provide a comprehensive and detailed explanation of Factorization techniques and how they are used in various real-life scenarios. Certainly, let's explore Chapter 1 on Complex Numbers in the Class 11th Mathematics book for the KPK Board in even greater detail: *1. Introduction to Complex Numbers:* Complex numbers are mathematical entities that extend the concept of real numbers. They consist of two parts: a real part (often denoted as 'a') and an imaginary part (denoted as 'bi,' where 'i' represents the square root of -1). The notation for a complex number is 'a + bi,' where 'a' and 'b' are real numbers. *2. Representation of Complex Numbers:* The complex number 'a + bi' can be visualized as a point in a two-dimensional plane called the complex plane. The real part 'a' corresponds to the horizontal axis (real axis), and the imaginary part 'bi' corresponds to the vertical axis (imaginary axis). This graphical representation allows students to understand complex numbers as points with both magnitude (distance from the origin) and direction (angle with respect to the positive real axis). *3. Arithmetic with Complex Numbers:* Addition and subtraction of complex numbers are straightforward. You add/subtract the real parts separately and the imaginary parts separately. For multiplication, you use the distributive property and the fact that 'i^2' equals -1. This results in a new complex number. Division involves multiplying the numerator and denominator by the conjugate (the complex number with the same real part but opposite imaginary part). This simplifies the division and eliminates the imaginary part in the denominator. *4. Modulus and Argument:* The modulus of a complex number 'z = a + bi' is denoted as |z| and is the distance of 'z' from the origin in the complex plane. It's calculated as the square root of the sum of the squares of 'a' and 'b.' The argument of 'z,' denoted as θ, is the angle formed by the line connecting the origin and 'z' with the positive real axis. It's measured in radians or degrees. The polar form of a complex number is often written as |z|(cos θ + i sin θ). *5. Conjugates:* The conjugate of a complex number 'a + bi' is 'a - bi.' Conjugates are used for various purposes, including simplifying complex number division and finding absolute values. *6. Practical Applications:* Complex numbers are widely used in electrical engineering for analyzing alternating current (AC) circuits. In physics, they are essential in quantum mechanics, where complex numbers represent probability amplitudes. They also appear in solving quadratic equations, even when the roots are complex. *7. Complex Plane:* The complex plane is a fundamental tool in understanding complex numbers. Students learn to plot complex numbers, calculate distances between them, and determine angles formed by complex numbers. This lecture also helpful forThe students of following boards: • All punjab boards • 1-Bahwal pur board • 2-Gujranwala board • 3-DG khan board • 4-Sarghoda board • 5-Faisalabad board • 6-Multan board • 7-Lahore board • 8-Rawalpindi board • 9-Sahiwal board Federal board(FBISE) , Allama Iqbal Open University (AIOU) kpk board and sindh board #11th #punjab board #sirshahzadsair #sirallahwasaya #ilmkidunya #waqasnasir #viralvideo #fbise #ilmkidunya YouTube channel link    / @syedwaqarhussainshah-mz7ti   Ex 1.1 Q1 to Q4 all parts link    • Class 11th Math EX 1.1 Q1 to Q4 FBISE & KP...   Ex 1.1 Q5 to Q7 all parts link    • Class 11th Math EX 1.1 Q5 to Q7 FBISE & KP...   Ex 1.1 Q8 to Q11 all parts link    • Class 11 Math EX 1.1 Q8 to Q11 FBISE & KPK...   Ex 1.2 Q1 to Q4 all parts link Ex 1.2 Q5 to Q6 all parts link Ex 1.2 Q7 to Q9 all parts link Ex 1.3 Q1 to Q3 all parts link Ex 1.3 Q4 to Q6 all parts link Ex Review Q1 to Q3 all parts link Ex Review Q4 to Q8 all parts #linkexercise 1.2 unit 1 complex number #1.2 first year mathematics KPK BOARDS #complex numbers unit 1 #chapter 1 ex 1.1class 11 #exercise 1.2 chapter 1 class 11 math #chapter 1 exercise 1.2 class 11