11Th Class Math New Book 2025 PCTB || Chapter 1 Exercise 1.5(Part-2

Описание: Polar coordinare system of a complex number, operations on complex numbers in polar form, complex numbers in the real world( voltage, current and resistance) cryptography
This video is for the students of fsc part 1 of punjab colleges and boards and this video contains exercise 1.5 of chapter 1 which is about complex numbers and it explains the concept of complex numbers and how to do operations on them and what is argand diagram and also how to factorize different polynomials.
#11thmath #11thmathnew
📘 Video Description:
This video is specially designed for FSC Part 1 students of Punjab Colleges and Boards. It covers Exercise 1.5 of Chapter 1 (Complex Numbers) in detail, along with important concepts that are frequently asked in board exams.

🔹 Topics Covered in this Video:
1️⃣ Polar Coordinate System of a Complex Number

Conversion from rectangular form
𝑧
=
𝑥
+
𝑖
𝑦
z=x+iy to polar form
𝑧
=
𝑟
(
cos
⁡
𝜃
+
𝑖
sin
⁡
𝜃
)
z=r(cosθ+isinθ).

Meaning of modulus
𝑟
=
∣
𝑧
∣
r=∣z∣ and argument
𝜃
=
arg
⁡
(
𝑧
)
θ=arg(z).

2️⃣ Operations on Complex Numbers in Polar Form

Multiplication and Division using polar form.

De Moivre’s Theorem for powers and roots of complex numbers.

3️⃣ Argand Diagram

Graphical representation of complex numbers.

Plotting real and imaginary parts on Cartesian plane.

4️⃣ Factorization of Polynomials using Complex Roots

Examples from Exercise 1.5 with step-by-step solutions.

5️⃣ Real-World Applications of Complex Numbers

Use in voltage, current, and resistance (AC circuits with phasors).

Importance of complex numbers in cryptography and data security.

📚 Why Watch This Video?
✔ Complete solution of Exercise 1.5 (Complex Numbers).
✔ Easy explanation of polar form, Argand diagram, and operations.
✔ Useful for Board Exams & Entry Tests (MDCAT/ECAT).
✔ Includes real-life examples to understand the practical use of complex numbers.