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| fsc:fsc_part_1_solutions:ch01 [2021/02/07 16:46] – created - external edit 127.0.0.1 | fsc:fsc_part_1_solutions:ch01 [2023/06/03 16:27] – [Solutions] Administrator |
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| 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://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]]) | 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]]) |
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| ====Solutions==== | ====Solutions==== |
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| * 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}} | * 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 1.2 (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}} | |
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| * 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}} | * 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}} |
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| {{tag>FSc FSc_Part1 Solutions_FSc_Part1}} | {{tag>FSc FSc_Part1 Solutions_FSc_Part1 Akhtar_Abbas}} |
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