====== Chapter 01: Number System ======
{{ :fsc:fsc_part_1_solutions:fsc-1-chap-01-ptb.jpg?nolink|Chapter 01: Number System}}
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) $\left(\frac{x_1+iy_1}{x_2+iy_2}\right)^n, x_2+iy_2\neq 0$ 

<callout type="tip" icon="true">
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 [[https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-imaginary-numbers-algebra-2/v/i-as-the-principal-root-of-1-a-little-technical|here]])
</callout>

====Solutions====
<callout type="success" icon="fa fa-download">
  * Exercise 1.1 (Handwritten) |  [[vfsc1>ch01:view&cp=01&p=09&ch=01&fp=Ex-1-1-FSC-part1-ver2|View Online]] | {{ :fsc:fsc_part_1_solutions:ex-1-1-fsc-part1-ver2.pdf |Download PDF}} ([[fsc-part1-ptb:sol:ch01:ex1-1|New Version]]) NEW
  * Exercise 1.2 (Handwritten) |  [[vfsc1>ch01:view&cp=01&p=05&ch=01&fp=Ex-1-2-FSC-part1-ver2|View Online]] | {{ :fsc:fsc_part_1_solutions:ex-1-2-fsc-part1-ver2.pdf |Download PDF}} ([[fsc-part1-ptb:sol:ch01:ex1-2|New Version]]) NEW
  * Exercise 1.3 (Handwritten) |  [[vfsc1>ch01:view&cp=01&p=05&ch=01&fp=Ex-1-3-FSC-part1-ver2|View Online]] | {{ :fsc:fsc_part_1_solutions:ex-1-3-fsc-part1-ver2.pdf |Download PDF}}    
</callout>

====Short Questions====
The following short questions of this chapter was send by Mr. [[people:akhtar]].
<callout type="success" icon="fa fa-download">
  * Chapter 01 | [[aafsc1>short-question-ch01-fsc-part1-akhtar-abbas|View Online]] | {{:fsc:fsc_part_1_mcqs:short-question-ch01-fsc-part1-akhtar-abbas.pdf|Download PDF}} NEW
</callout>
====Here is next chapter====
<grid>
<col sm="4"><thumbnail>
[[:fsc:fsc part 1 solutions:ch02|{{:fsc:fsc_part_1_solutions:fsc-1-chap-02-ptb.jpg?250}}]]
<caption>
**[[:fsc:fsc part 1 solutions:ch02]]**
</caption>
</thumbnail></col>
</grid>
{{tag>FSc FSc_Part1 Solutions_FSc_Part1}}