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The Fundamantal Theorem of Algebra: |
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The Fundamantal Theorem of Algebra: |
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<math>a_n \times z^{n} + a_n-1 \times z^{n-1} + \dots + a_0</math> |
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<math>a_n \times z^{n} + a_n-1 \times z^{n-1} + \dots + a_0</math> |
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where <math>a_i \in C and a_i != 0</math> has a soluion <math>z \in C</math> |
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where <math>a_i \in C </math>and<math> a_i != 0</math> has a soluion <math>z \in C</math> |
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In particular, <math>z^{2} - 1 = 0</math> has a solution. |
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In particular, <math>z^{2} - 1 = 0</math> has a solution. |
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Revision as of 23:04, 24 September 2014
Polar coordinates:
![{\displaystyle r\times e^{i\theta }=r\times cos\theta +i\times rsin\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/bb3fe12b7abc1bc87939455defa0f886e9a426ae)
![{\displaystyle r_{1}\times e^{i\theta _{2}}=r_{1}\times (cos\theta +sin\theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/468b17fbb162ee9c6fa30873a69a4883723a5743)
The Fundamantal Theorem of Algebra:
where
and
has a soluion
In particular,
has a solution.
- Forces can multiple by a "scalar"(number).
No "multiplication" of forces.
Definition of Vector Space:
A "Vector Space" over a field F is a set V with a special element
and two binary operations:
![{\displaystyle +:V\times V->V}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d5969788edd165631a0c7c5fbc249dce78e5206)
![{\displaystyle \times :V\times V->V}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b2747ffcfd962547656ac0ca993731463f2b5da)
s.t.
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