Class 10 Maths Exercise 1.1 (NBF 2025) | Chapter 1 Complex Numbers | 1.1 maths 10 FBISE | Engr Ahmed

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## Description

In this video, we solve **Class 10 Maths Chapter 1 – Exercise 1.1 (Complex Numbers)** from the **NBF 2025 Edition (FBISE)** step by step in a clear and exam-focused method.

This lecture is specially prepared for **FBISE Class 10 students (Federal Board 2025 syllabus)**.

You will learn:
• Square roots of negative numbers
• Expressing answers in terms of i
• Addition and subtraction of complex numbers
• Multiplication of complex numbers
• Powers of i shortcut method
• Writing answers in a + bi form
• Division of complex numbers (rationalization method)

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## 📌 Recommended Lectures (Must Watch)

🔹 Complex Numbers – From Basics (Operations + Imaginary Numbers)
[https://youtu.be/bLYUIJKMzIQ?si=lXLZlw3Kdtu6O5YL](https://youtu.be/bLYUIJKMzIQ?si=lXLZlw3Kdtu6O5YL)
This video explains complex numbers from basics and their operations. Ideal before starting Exercise 1.1.

🔹 Number System Explained with Tree | Real, Rational, Irrational & Complex Numbers
[https://youtu.be/JzTR1jPw_TU?si=_r1tmrvagFjfPiw7](https://youtu.be/JzTR1jPw_TU?si=_r1tmrvagFjfPiw7)
This lecture explains the complete number system using a tree method and shows where complex numbers fit.

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## ⏱️ Detailed Timeline (Question-wise)

0:00 – Introduction (FBISE Class 10 | NBF 2025)

### Question 1: Simplify and express in terms of i

0:47 – Q1(i) √−3
1:33 – Q1(ii) 6√−4
2:10 – Q1(iii) √(4/−9)
2:55 – Q1(iv) −√−20
4:36 – Q1(v) 4 − √−60
6:20 – Q1(vi) √−8 × √−2

### Question 2: Simplify

7:52 – Q2(i) (4 − i) + (5 + 5i)
9:04 – Q2(ii) (7 − 6i) − (5 − 6i)
9:52 – Q2(iii) (−2 + 8i) − (7 + 3i)
10:35 – Q2(iv) (4 − 2i) − (5 − 2i)
11:41 – Q2(v) (2 + 4i)(1 + 2i)
13:12 – Q2(vi) (1 − 4i)(2 − 3i)
14:20 – Q2(vii) −8i(2 − 2i)
15:35 – Q2(viii) (3 + 2i)²
17:36 – Q2(ix) (3 − 6i)(3 + 6i)
18:55 – Q2(x) (−5 − 3i)²
20:40 – Q2(xi) (1 + √2 i)(1 − √3 i)
23:18 – Q2(xii) (√2 + i)(√2 − i)

### Question 3: Powers of i

24:10 – Q3(i) i⁹
26:19 – Q3(ii) i¹³
27:03 – Q3(iii) i²⁸
28:04 – Q3(iv) (−i)²¹
28:43 – Q3(v) (3i)³
29:44 – Q3(vi) (−2i)⁴

### Question 4: Simplify in the form a + bi

30:45 – Q4(i) 9 + i⁶
31:27 – Q4(ii) −17 + i⁵
32:04 – Q4(iii) i⁴ − 13i
32:52 – Q4(iv) i⁸ + 21i
33:39 – Q4(v) i⁵ + i⁷
34:50 – Q4(vi) i⁷⁴ − i¹⁰⁰

### Question 5: Divide and simplify in a + bi form

36:01 – Q5(i) 3 / (4 − i)
37:37 – Q5(ii) 3i / (6 + 5i)
40:08 – Q5(iii) (3 − i√5) / (3 + i√5)
44:19 – Q5(iv) (2 + 7i) / 5i
46:42 – Q5(v) (4 + 5i) / (4 − 5i)
49:00 – Q5(vi) (3 + 2i) / (2 + i)
51:14 – Q5(vii) (5 + i) / (1 + 2i)
53:16 – Q5(viii) (a + ib) / (a − ib)
55:42 – Q5(ix) (1 + i) / (1 − i)²
58:34 – Q5(x) (2 + 2i)² / (1 + i)²

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## ✅ Hashtags

#FBISE #Class10Maths #NBF2025 #MathsChapter1 #Exercise1_1 #ComplexNumbers #ImaginaryNumbers #PowersOfi #aPlusbi #BoardExam2025 #FederalBoard #EngrAhmed

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Видео Class 10 Maths Exercise 1.1 (NBF 2025) | Chapter 1 Complex Numbers | 1.1 maths 10 FBISE | Engr Ahmed канала Engr Ahmed