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fsc:fsc_part_1_solutions:ch01 [2022/09/27 13:45] – [Solutions] Dr. Atiq ur Rehman | fsc:fsc_part_1_solutions:ch01 [2023/06/03 16:30] (current) – Administrator | ||
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====== Chapter 01: Number System ====== | ====== Chapter 01: Number System ====== | ||
{{ : | {{ : | ||
- | Notes (Solutions) of Chapter 01: Number System, | + | Notes (Solutions) of Chapter 01: Number System, |
==== Contents & summary ==== | ==== Contents & summary ==== | ||
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* Operation on complex numbers | * Operation on complex numbers | ||
* Complex numbers as ordered pairs of real numbers | * Complex numbers as ordered pairs of real numbers | ||
- | * Properties of the foundamental | + | * Properties of the fundamental |
* A special subset of $\mathbb{C}$ | * A special subset of $\mathbb{C}$ | ||
* The real line | * The real line | ||
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<callout type=" | <callout type=" | ||
Did you know $\sqrt{-1}=i$ is misleading? | 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 [[https:// | + | 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 $\sqrt{-1}=i$ |
</ | </ | ||
====Solutions==== | ====Solutions==== | ||
<callout type=" | <callout type=" | ||
- | * Exercise 1.1 (Handwritten) | [[vfsc1> | + | * Exercise 1.1 (Handwritten) | [[vfsc1> |
- | + | * Exercise 1.2 (Handwritten) | [[vfsc1> | |
- | * Exercise 1.2 (Handwritten) | [[vfsc1> | + | |
- | | + | |
* Exercise 1.3 (Handwritten) | [[vfsc1> | * Exercise 1.3 (Handwritten) | [[vfsc1> | ||
- | </ | ||
- | |||
- | ===Notes by Akhtar Abbas=== | ||
- | The following notes are provided by Mr. Akhtar Abbas. These notes are part of {{https:// | ||
- | <callout type=" | ||
- | * Exercise 1.2 | {{ : | ||
- | |||
- | * Exercise 1.4 | {{ : | ||
</ | </ | ||