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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 {{Ucademy Smart learning App|https:// | ||
| - | <callout type=" | ||
| - | * Exercise 1.2 | {{ : | ||
| - | |||
| - | * Exercise 1.4 | {{ : | ||
| </ | </ | ||