Exercise 1.2 Class 11 Math Solutions - Unit 1 Complex Numbers, Punjab Board
Step-by-step solutions to Exercise 1.2, Unit 1: Complex Numbers, for Class 11 Punjab Board students. Covers the equality of two complex numbers, solving equations for real variables x and y, and finding the square root of complex numbers worked out question by question.
Exercise Overview
Exercise 1.2 advances Unit 1 of Class 11 Mathematics by focusing on two central algebraic competencies: solving complex equations using the equality condition and computing the square roots of complex numbers. The equality theorem states that two complex numbers a + bi and c + di are equal if and only if their real parts are equal (a = c) and their imaginary parts are equal (b = d). Students often encounter algebraic hurdles when solving non-linear systems resulting from quadratic relations during square root calculations.
The exercise questions are primarily divided into solving equations for real variables x and y and evaluating square roots of expressions such as a + bi. Finding the square root involves assuming √(a + bi) = x + iy, expanding to get x² - y² = a and 2xy = b, and systematically solving for the pair of real values (x, y). Careful consideration must be given to the sign of b to ensure the correct pairing of positive and negative roots.
For Punjab Board HSSC Part 1 examinations, Exercise 1.2 is a regular source of high-scoring short questions and long questions across Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, and other affiliated boards. Mastering these step-by-step solutions ensures students develop strong equation-solving proficiency and algebraic accuracy for annual board examinations.