Exercise 1.2 Class 10 Math Solutions – Unit 1 Complex Numbers, Punjab Board

Exercise 1.2 expands directly on foundational concepts introduced in Unit 1, moving from the definition and rectangular form of complex numbers into full algebraic operations. For Class 10 Punjab Board students, this exercise teaches how to manipulate complex quantities arithmetically – covering scalar multiplication, addition, subtraction, multiplication, and quotient division. Addition and subtraction require students to group real parts and imaginary parts independently, ensuring a solid grasp of how components behave under standard arithmetic.

Multiplication and division form the core focus of Exercise 1.2. In multiplication, students expand binomial products and apply the fundamental identity i² = -1 to simplify expressions back into standard rectangular form a + bi. Division introduces the essential technique of multiplying the numerator and denominator by the complex conjugate of the denominator, thereby rationalizing the divisor into a purely real number. The exercise also rigorously tests fundamental algebraic properties such as closure, commutativity, associativity, and distributivity across the complex number system.

In Punjab Board examinations (including Lahore, Rawalpindi, Faisalabad, and Gujranwala Boards), questions from Exercise 1.2 frequently feature in both objective MCQs and subjective short and long questions. Board examiners often test division of complex expressions and verification of distributive or commutative laws. Working through these step-by-step solutions ensures students build thorough problem-solving fluency and avoid common sign errors before advancing to subsequent unit exercises.