Exercise 1.4 Class 10 Math Solutions – Unit 1 Complex Numbers, Punjab Board
Step-by-step solutions to Exercise 1.4 of Unit 1: Complex Numbers for Class 10 Punjab Board students. Covers extracting real and imaginary parts from powers and quotients of complex numbers, and solving simultaneous linear equations with complex coefficients.
Exercise Overview
Exercise 1.4 introduces advanced algebraic techniques for working with complex numbers in Unit 1. Class 10 Punjab Board students advance from standard arithmetic into higher power expansions of the form (x + iy)ⁿ and fractional expressions ((x₁ + iy₁) / (x₂ + iy₂))ⁿ. The core objective of these questions is to systematically manipulate multi-term expressions until they are cleanly separated into their constituent real and imaginary parts.
To handle fractional expressions raised to powers, students must first rationalize the denominator by multiplying both numerator and denominator by the complex conjugate. Once simplified into a standard a + bi format, the expression is expanded using exponent laws and i² = -1 substitutions. In addition, Exercise 1.4 addresses systems of simultaneous linear equations with complex coefficients, where students employ elimination or substitution techniques and equate corresponding real and imaginary components across equations to solve for unknown variables.
In Punjab Board examinations (including Lahore, Rawalpindi, Gujranwala, Faisalabad, and Multan Boards), questions from Exercise 1.4 are prime candidates for high-scoring subjective long questions. Examiners frequently select simultaneous equations or multi-step power simplifications to test precision and algebraic fluency. Practicing these step-by-step solutions ensures students develop the rigorous problem-solving skills required for top exam grades.