Chapter 01: Number System

Chapter 01: Number System Notes (Solutions) of Chapter 01: Number System, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.

  • 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 foundamental 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 $\sqrt{-1}=i$. (see detail answer here)

Notes by Akhtar Abbas

The following notes are provided by Mr. Akhtar Abbas. These notes are part of Ucademy Smart learning App available for android devices.

The following short questions of this chapter was send by Mr. Akhtar Abbas.

  • fsc/fsc_part_1_solutions/ch01
  • Last modified: 29 hours ago
  • by Dr. Atiq ur Rehman