FBISE 10th Class Mathematics Exercise 1.2 Solution (Complex Numbers)

About this book

This is a 21-page, fully worked solution set to Exercise 1.2 (Complex Numbers) from the FBISE Class 10 / Matric Part 2 Mathematics textbook — Chapter 1. It covers all 11 questions across every part, with every algebraic step shown and a boxed final answer, so you can check your own working line by line rather than just seeing a final result.

The exercise walks through additive and multiplicative inverses of complex numbers, verifying that two complex numbers are multiplicative inverses by multiplying them out, finding the multiplicative inverse using the conjugate method (including cases where the denominator isn't a simple integer), multiplying a complex number by its own conjugate to confirm the result is always real, plotting complex numbers on the Argand diagram, and the four standard conjugate identities — for example that z·z̄ is always real, that |z| equals |−z| equals |z̄|, and that z² − (z̄)² is always purely imaginary — proved both for specific numbers and in general for any z = a + bi.

Later questions cover representing the sum and difference of two complex numbers graphically using the parallelogram law, and representing a product of two complex numbers as a third vector on the same Argand diagram. Where a result has a notable pattern — such as a division that simplifies to a clean integer, or an identity that holds for every complex number — a short explanatory note is added after the answer, not just the working.