This is a first unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions.
Recall complex number $z$ represented by an expression of the form $z=a+ib$ or of the form $(a,b)$ where $a$ and $b$ are real numbers and $i=\sqrt{-1}$.
Recognize $a$ as real part of $z$ and $b$ as imaginary part of $z$.
Know condition for equality of complex numbers.
Carry out basic operations on complex numbers.
Define $\bar{z} = a —ib$ as the complex conjugate of $z=a+ib$.
Define $|z| = \sqrt{a^2+b^2}$ as the absolute value or modulus of a complex number $z=a+ib$
Describe algebraic properties of complex numbers (e.g. commutative, and distributive) with respect to $'+'$ and $'\times'$.
Know additive identity and multiplicative identity for the set of complex numbers.
Find additive inverse and multiplicative inverse of a complex $z$.
Demonstrate the following properties $|z|=|-z|=|\bar{z}=|-\bar{z}|$
Find real and imaginary parts of complex numbers.
Solve simultaneous linear equations with complex coefficients.
Write the polynomial as a product of linear factors.
Solve quadratic equation of the form $pz^2+ qz+ r = 0$ by completing squares, where $p,q,r$ are real numbers and $z$ a complex number.