Notes (Solutions) of Chapter 01: Number System, Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
Rational numbers and irrational numbers
Properties of real numbers
Complex numbers
Operation on complex numbers
Complex numbers as ordered pairs of real numbers
Properties of the fundamental operations on complex numbers
A special subset of $\mathbb{C}$
The real line
Real plane or coordinate plane
Geometrical representation of complex numbers, the complex plane
To find real and imaginary parts of (i) $(x+iy)^n$ (ii) $\left(\frac{x_1+iy_1}{x_2+iy_2}\right)^n, x_2+iy_2\neq 0$
Did you know $\sqrt{-1}=i$ is misleading?
The square root of complex number has many values with two distinct values. $\sqrt{-1}$ has two distinct values $i$ and $-i$. This fact can be verified by taking square of $i$ and $-i$, which give the same answer $-1$. It is different to say $i^2=-1$ and $\sqrt{-1}=i$ unless we define $\sqrt{-1}$ as principal square root of complex number. (see detail answer here)