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.

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 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)

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