## Unit 01: Complex Numbers (Solutions)

This is a first unit of the book Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. On this page we have provided the solutions of the questions.

After reading this unit the students will be able to

- Recall complex number $z$ and recognize its real and imaginary part.
- Know the condition for equality of two complex numbers.
- Revising the basic operations on complex numbers.
- Find conjugate and modulus of a complex number.
- Solve the simultaneous linear equations with complex coefficients.
- Factorize the given polynomials like $z^2+a^2$ or $z^3-3z^2+z=5$
- Solve quadratic equation of the form $pz^2+qz+r=0$, by completing squares, where $p,q,r$ are real numbers and $z$ is a complex number.
- Represent complex numbers in polar coordinates.
- Applying the binary operations in polar form.
- Solve complex equations and inequations in polar form.
- Using the complex numbers in real world problems.