Class 10 Maths Chapter 1 Review Exercise 1 Solutions 2026 – Complex Numbers Notes PDF
Unit 1: Complex Numbers | Review Exercise 1 | Punjab Board New Syllabus 2026–27
Updated August 2026: Review Exercise 1 solutions for Complex Numbers have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.
Putting the Whole Chapter Together
Each exercise so far has focused on one skill at a time — definitions in 1.1, operations in 1.2, conjugates and division in 1.3, modulus and argument in 1.4. Review Exercise 1 removes those labels and mixes everything together, the same way a real board exam question can quietly combine two or three ideas in a single problem. It is less about learning something new and more about proving the earlier exercises actually stuck.
What This Review Exercise Draws On
Definitions and Standard Form
Quick-recall questions on identifying the real part, imaginary part, and standard form of a complex number, exactly as first introduced in Exercise 1.1.
Operations in Combination
Problems that chain addition, subtraction, and multiplication together, sometimes inside the same expression, requiring careful attention to the order of operations.
Conjugates and Division
Mixed questions involving finding a conjugate, using it to divide two complex numbers, or applying the identity |z|² = z × z̄ from Exercise 1.3.
Modulus, Argument, and Polar Form
Problems that ask for the modulus or argument of a result obtained after first performing an operation — for example, multiply two complex numbers, then find the modulus of the answer.
Step-by-Step Solved Examples
Q. No. 1: If z₁ = 2 + 3i and z₂ = 1 − i, find |z₁ + z₂|.
z₁ + z₂ = (2 + 1) + (3i − i) = 3 + 2i
|z₁ + z₂| = √(3² + 2²) = √(9 + 4) = √13
Q. No. 2: Find the conjugate of z = (2 + i)(1 − 3i), then state its real and imaginary parts.
First expand: (2 + i)(1 − 3i) = 2 − 6i + i − 3i² = 2 − 5i + 3 = 5 − 5i
So z = 5 − 5i, and its conjugate z̄ = 5 + 5i
Re(z̄) = 5, Im(z̄) = 5
Q. No. 3: Simplify i¹⁰⁰ and state whether the result is real or imaginary.
Powers of i repeat every 4 terms: i¹=i, i²=−1, i³=−i, i⁴=1
100 ÷ 4 = 25 remainder 0, so i¹⁰⁰ = i⁴ = 1
The result, 1, is a real number.
These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Review Exercise 1 in the same numbered, step-by-step format.
MCQs, Short Questions & Long Questions from This Review
Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:
- MCQs: Rapid-fire recall across all four exercises, useful for timed practice
- Short Questions: Two-step problems combining any two of the chapter’s core ideas
- Long Questions: Full multi-part problems that mirror the structure of an actual board exam question
Study Tips for Reviewing This Chapter
- Attempt Review Exercise 1 only after completing Exercises 1.1 through 1.4 — it assumes all four are already familiar
- Keep a separate practice notebook for working through mixed questions, since seeing your own worked steps helps more than reading solved ones
- Revise in the same order as the textbook — definitions, then operations, then conjugate/division, then modulus/argument — so each new idea builds on the last
- Re-attempt any question you got wrong the next day, rather than only reading the correct answer once
Common Mistakes Students Make in Review Exercise 1
- Trying to answer a multi-step question in one line instead of solving it operation by operation
- Applying a rule from the wrong exercise — for example, using the modulus formula on a question that only asks for the conjugate
- Rushing through sign changes when two or more operations are chained together
Why This Exercise Matters for the Board Exam
Board papers rarely test a single concept in isolation, which is exactly what Review Exercise 1 simulates. Working through it carefully is one of the best ways to confirm genuine readiness for Chapter 1 before moving on to Chapter 2.
Quick Links – Rest of Chapter 1: Complex Numbers
| Section | Covers |
| Exercise 1.1 | Standard form, real & imaginary parts, i |
| Exercise 1.2 | Addition, subtraction & multiplication |
| Exercise 1.3 | Conjugate, division & Argand diagram |
| Exercise 1.4 | Modulus, argument & polar form |
| Review Exercise 1 | You are here |
| Chapter 1 MCQs | Objective-type practice |
Links for sections other than Review Exercise 1 will be activated as they are published on this site.
Download Review Exercise 1 Notes PDF
Click below to view or download the complete Review Exercise 1 notes in PDF format.
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Frequently Asked Questions (FAQs)
Q1. Are these Review Exercise 1 notes free to download?
Yes, all notes on this page are completely free to view and download in PDF format.
Q2. Which board are these notes for?
These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).
Q3. When should I attempt Review Exercise 1?
Only after completing all four exercises (1.1 to 1.4), since the questions here mix topics from across the chapter without labeling which exercise each one came from.
Q4. Does this page include MCQs and short questions too?
Yes, the uploaded notes include MCQs, short questions, and long questions covering the whole chapter, organized by question type to match the board paper pattern.
Q5. How can I download the PDF?
Click the “Download PDF” button above and the notes will open or download directly to your device.
Q6. Are these notes updated for the new 2026–27 syllabus?
Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.
Comments & Feedback
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