Exercise 1.3 Class 10 Math Solutions – Unit 1 Complex Numbers, Punjab Board

Step-by-step solutions to Exercise 1.3 of Unit 1: Complex Numbers for Class 10 Punjab Board students. Covers the Argand plane, geometric and algebraic conjugate of complex numbers, modulus calculations, and their core properties.

This page provides complete solved solutions for Exercise 1.3 from Unit 1: Complex Numbers, Class 10 Mathematics, Punjab Board (PCTB). It covers the Argand plane, geometric representation and properties of complex conjugates, and modulus calculation with its properties. Every question is solved step by step for Matric Part 2 students preparing for Punjab Board exams.
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Exercise Overview

Exercise 1.3 introduces the geometric interpretation of complex numbers alongside critical algebraic tools in Unit 1. Class 10 Punjab Board students learn how complex numbers exist on the Complex or Argand Plane, where the horizontal axis represents real components and the vertical axis represents imaginary components. By treating a complex number z = a + bi as an ordered pair (a, b), students build a visual bridge between coordinate geometry and complex algebra.

The exercise thoroughly explores the concept of the complex conjugate z̄ = a - bi and its geometric meaning as a reflection across the real axis. Students practice verifying fundamental conjugate properties across additions, subtractions, and multiplications. In addition, Exercise 1.3 focuses heavily on the modulus of a complex number |z| = √(a² + b²), which measures the exact geometric distance from the origin to the point (a, b). Key relationships like z · z̄ = |z|² and multiplicative modulus rules |z₁ · z₂| = |z₁| · |z₂| are rigorously evaluated through textbook problems.

For Punjab Board examinations (such as Lahore, Rawalpindi, Gujranwala, and Faisalabad Boards), questions from Exercise 1.3 are essential for securing marks. Modulus formulas, conjugate properties, and Argand plane plotting are standard components in both objective MCQs and subjective short and long questions. Studying these step-by-step solutions gives students the analytical clarity needed for flawless exam performance.

FAQs

Are these Exercise 1.3 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all prescribed Exercise 1.3 topics in Unit 1 for the 2026-2027 session.
Do these solutions cover every question in Exercise 1.3?
Yes, every problem in Exercise 1.3 is fully solved in order, detailing Argand plane plotting, conjugate calculations, and modulus proofs step by step.
What is the Argand plane in Exercise 1.3?
The Argand plane is a two-dimensional geometric plane where the horizontal axis represents real numbers and the vertical axis represents imaginary numbers, allowing complex numbers to be plotted as points (a, b).
How is the conjugate of a complex number represented geometrically?
Geometrically, the conjugate of a complex number z = a + bi is z̄ = a - bi, which represents the reflection of the point (a, b) across the real (horizontal) axis in the Argand plane.
How do you calculate the modulus of a complex number?
The modulus of z = a + bi is denoted by |z| and calculated as √(a² + b²), representing the geometric distance from the origin (0, 0) to the point (a, b) in the Argand plane.
Can students read these solutions online?
Yes, the full Exercise 1.3 solution set is available to read online on this page with no separate download required.
Are these solutions useful for Punjab Board exams?
Yes. Questions on finding conjugates, calculating modulus, and verifying modulus/conjugate properties frequently appear in short and long questions in Punjab Board papers.
Are these solutions based on the latest PCTB / PECTAA syllabus?
Yes, they are aligned with the current PCTB and PECTAA Mathematics syllabus for the 2026-2027 academic session for Class 10.
Are these Exercise 1.3 solutions free for students?
Yes, Exercise 1.3 solutions on MaryamNotes.pk are completely free to read online for all Class 10 students across Lahore, Rawalpindi, Gujranwala, Faisalabad, and all Punjab boards.