Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN.
A complex number is an element $(x,y)$ of the set $$ \mathbb{R}^2=\{(x,y): x,y \in \mathbb{R}\} $$ obeying the following rules of addition and multiplication.
For $z_1=(x_1,y_1)$, $z_2=(x_2,y_2)$, we put
The set $\mathbb{R}^2$ with operation defined above is denoted by $\mathbb{C}$.