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This commit is contained in:
Alier 2025-09-09 11:50:10 +02:00
parent be225c47a4
commit 2d97894f0a
28 changed files with 44163 additions and 72 deletions
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5
.obsidian/canvas.json vendored Normal file
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@ -0,0 +1,5 @@
{
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2
.obsidian/graph.json vendored
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12
.obsidian/plugins/obsidian-excalidraw-plugin/data.json vendored
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@ -39,11 +39,11 @@
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69
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@ -4,33 +4,21 @@
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4
Apuntes.md
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@ -2,6 +2,8 @@ Arnau Alier Torres
# Introducción a Química
### [[Química/Introducción Química|Introducción Química]]
### [[Química/Introducción Química|Química]]
### [[Introducción Quimica/Introducción Química|Introducción Química]]
## [[Física/Física|Física]]
## [[Matematicas/Números complejos|Números complejos]]

2
Física/Cinematica.md
View File

@ -32,7 +32,7 @@ $$
# Aceleración constante
![[../Pasted image 20250909095158.png]]
![[../Resources/Pasted image 20250909095158.png]]
# Movimiento Circular
- Coordenadas cartesianas (x, y)

102
Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md
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261
Ilustraciónes/Mates 09-09-25_10.excalidraw.md Normal file
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---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
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%%
## Drawing
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%%

2
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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
%%
## Drawing
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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
%%
## Drawing
```json
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En los casos donde se quiere resolver equitación del estilo $x²+4=0$, nos encontraremos en casos donde $x=\sqrt{-4}$, para eso asignamos un numero $i=\sqrt{-1}$ , que lo nombramos numero imaginario.
Esto nos da que para toda $p(x)=cte$ (Tiene solución).
- Un numero complejo se declara como $a+b_i$, con a y be siendo $R$.
- El modulo de un numero complejo es $|z|=\sqrt{a²+b²}$
![[../Ilustraciónes/Números complejos 09-09-25_10.excalidraw.svg|300]]
%%[[../Ilustraciónes/Números complejos 09-09-25_10.excalidraw.md|🖋 Edit in Excalidraw]]%%
- Un numero complejo conjugado consiste en cambiar de símbolo un numero imaginario $\overline{z}=a-b_i$
- z multiplicado por su conjugado $\overline{z}$ , $z*\overline{z}=|z|²$
$$
\huge z\overline{z}=(a+bi)(a-bi)=a²-(bi)²=a²+b²=|z|²
$$
Ejemplo
![[../Ilustraciónes/Números complejos 09-09-25_10_0.excalidraw.svg]]
%%[[../Ilustraciónes/Números complejos 09-09-25_10_0.excalidraw.md|🖋 Edit in Excalidraw]]%%
## Forma polar
La forma polar es una forma alternativa de representar a un numero complejo
![[../Ilustraciónes/Números complejos 09-09-25_10_1.excalidraw.svg|300]]
%%[[../Ilustraciónes/Números complejos 09-09-25_10_1.excalidraw.md|🖋 Edit in Excalidraw]]%%
El angulo que forma el eje Ox es el argumento(arg) de z, por lo tanto, $|z|$ y $\alpha$ definen el numero complejo z
$$
\huge r_{\alpha} \cdot r'_{\alpha '}=(r\cdot r') => |z\cdot z'|=|z|\cdot |z'|
$$
Comprobación:
![[../Ilustraciónes/Números complejos 09-09-25_11_0.excalidraw.svg]]
%%[[../Ilustraciónes/Números complejos 09-09-25_11_0.excalidraw.md|🖋 Edit in Excalidraw]]%%
$$
\huge arg(z z')=arg z + arg z'
$$
>[!NOTE] Nota
>Multiplicar por i equivale a rotar 90
>$(3+2i)\cdot i=-2+3i$
$$
\huge\frac{r_\alpha}{r'_\alpha}=(\frac{r}{r'})_{\alpha-\alpha'}
$$
## Potencias
Para calcular la potencia de un numero real se usa
$$
\huge (r_\alpha)^\mu=r^{\mu}_{\mu\alpha}
$$
Ejemplo
$$
\huge(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i)^{100}=1_{100\frac{\pi}{4}}
$$
![[../Ilustraciónes/Números complejos 09-09-25_11_1.excalidraw.svg|200]]
%%[[../Ilustraciónes/Números complejos 09-09-25_11_1.excalidraw.md|🖋 Edit in Excalidraw]]%%
# Raíz n-esima
Para calcular la raíz n-esima se utiliza
$$
\huge^{\mu}\sqrt{r_\alpha}=r'_{\alpha'}
$$
tal que $r'^{\mu}=r$ $\mu\alpha'=\alpha(+k2\pi)$

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