Introduction
The best Unit 1, Complex Numbers, solved notes for Class 11 Punjab Boards are now available, with 100 percent of exercises solved using easy, step by step solutions, diagrams, and the marking scheme, based on the new book from PECTAA, the Punjab Curriculum and Textbook Board. These notes are perfect for the 2027 exams and are built to help students score 90 plus marks.
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Ideal for Students, Teachers, and Lecturers Across All Nine Punjab Boards
These notes are used at top registered institutions across all nine Punjab boards, including Military College Jhelum under the Rawalpindi Board, Cadet College Okara under the Sahiwal Board, Cadet College Sargodha under the Sargodha Board, Cadet College Jhang under the Faisalabad Board, Cadet College Pasrur under the Gujranwala Board, Garrison Cadet College Kohat, Cadet College Spinkai under the DG Khan Board, Aitchison College Lahore, Sadiq Public School Bahawalpur, Forman Christian College Lahore, Government College University Faisalabad, Army Public Schools and Colleges, and Beaconhouse, Lahore Grammar School, The City School, and Roots Ivy, among many others.
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Exercise 1.1, Multiplicative Inverse and Real and Imaginary Parts
All questions in Exercise 1.1 are fully solved, covering how to find the multiplicative inverse of a complex number and how to identify the real and imaginary parts of the results of complex operations.
| Question | Problem | Solution |
|---|---|---|
| Q1(i) | The multiplicative inverse of the complex number negative 4, 7 | negative 4 over 65, minus 7 over 65 i |
| Q1(ii) | The multiplicative inverse of the complex number root 2, negative root 5 | root 2 over 7, plus root 5 over 7 i |
| Q1(iii) | The multiplicative inverse of the complex number 1, 0 | 1 |
| Q2(i) | The quantity 2 minus 7i, divided by the quantity 4 plus 5i | negative 27 over 41, minus 38 over 41 i |
| Q2(ii) | The quantity negative 2 plus 3i, squared, divided by the quantity 1 plus i | negative 17 over 2, minus 7 over 2 i |
The full solved PDF for Exercise 1.1 is available, covering every question and part in complete detail.
All Remaining Exercises, Plus the Review Exercise, 100 Percent Solved
- Exercise 1.2, Properties and Operations of complex numbers.
- Exercise 1.3, Modulus and Argument of a complex number.
- Exercise 1.4, Polar Form of complex numbers.
- Exercise 1.5, De Moivre’s Theorem and Powers of complex numbers.
Bonus Resources
- A Complex Numbers formula sheet PDF for quick reference.
- The top 30 complex number shortcuts for faster problem solving.
- Complex Numbers video lectures.
- Unit 2, Functions and Graphs, is coming soon as the next unit in this series.
Complex Numbers
Complex numbers are an extension of the real number system that allow us to solve equations that do not have real solutions. A complex number is written in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit defined by iĀ² = ā1. For example, 3 + 2i is a complex number with real part 3 and imaginary part 2.
In this unit, students learn how to add, subtract, multiply, and divide complex numbers. They also study the concept of the complex conjugate, which is useful when simplifying expressions and performing division. The modulus of a complex number represents its distance from the origin and helps students understand complex numbers geometrically.
Students also learn how complex numbers can be represented on the Argand plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. This provides a visual way to understand complex numbers.
Complex numbers are widely used in mathematics, physics, engineering, electrical circuits, signal processing, and computer science. By studying this unit, students develop a stronger understanding of algebra and prepare for more advanced mathematical concepts.
View the Full Solved PDF
The complete, original solved PDF for Unit 1 is available to view for free.
Why This Unit Matters for Your Overall Score
Complex Numbers is the opening unit of the Class 11 Mathematics syllabus, and mastering operations like the multiplicative inverse, along with separating real and imaginary parts as shown in Exercise 1.1, builds the foundation needed for the modulus, argument, and polar form work covered later in Exercise 1.3 and 1.4.
De Moivre’s Theorem and the nth roots of unity, covered in Exercise 1.5 and 1.6, then build directly on this polar form understanding, which is why working through the exercises in order makes the more advanced later sections far more approachable.
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Frequently Asked Questions
Which exercises are covered in these Unit 1 notes? Exercise 1.1 through Exercise 1.5 are all covered in full, with complete step by step solutions.
How do I find the multiplicative inverse of a complex number? Multiply the numerator and denominator by the conjugate of the complex number, then divide both the real and imaginary parts by the resulting real denominator, as shown in the Q1 examples above.
Are past papers included with these notes? Yes, Unit 1 past papers solved from 2018 through 2025 are included as a bonus resource.
Do I need to download the PDF to view these notes? The full solved PDF can be viewed directly on the site for free.
Conclusion
With Exercise 1.1 through Exercise 1.5 fully solved, Class 11 students across all nine Punjab boards have a complete, exam ready resource for mastering Complex Numbers ahead of the 2026 exams. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!