diff --git a/.obsidian/canvas.json b/.obsidian/canvas.json new file mode 100644 index 0000000..bfc50b8 --- /dev/null +++ b/.obsidian/canvas.json @@ -0,0 +1,5 @@ +{ + "snapToObjects": true, + "snapToGrid": true, + "defaultWheelBehavior": "zoom" +} \ No newline at end of file diff --git a/.obsidian/graph.json b/.obsidian/graph.json index 610cffc..bea08a2 100644 --- a/.obsidian/graph.json +++ b/.obsidian/graph.json @@ -17,6 +17,6 @@ "repelStrength": 20, "linkStrength": 1, "linkDistance": 250, - "scale": 0.49067524999463263, + "scale": 0.3147925906523868, "close": false } \ No newline at end of file diff --git a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json index 24b0358..7f5cbb2 100644 --- a/.obsidian/plugins/obsidian-excalidraw-plugin/data.json +++ b/.obsidian/plugins/obsidian-excalidraw-plugin/data.json @@ -39,11 +39,11 @@ "dynamicStyling": "colorful", "isLeftHanded": false, "iframeMatchExcalidrawTheme": true, - "matchTheme": false, - "matchThemeAlways": false, - "matchThemeTrigger": false, + "matchTheme": true, + "matchThemeAlways": true, + "matchThemeTrigger": true, "defaultMode": "normal", - "defaultPenMode": "never", + "defaultPenMode": "always", "penModeDoubleTapEraser": true, "penModeSingleFingerPanning": true, "penModeCrosshairVisible": true, @@ -52,7 +52,7 @@ "renderImageInHoverPreviewForMDNotes": false, "renderImageInMarkdownToPDF": false, "allowPinchZoom": false, - "allowWheelZoom": false, + "allowWheelZoom": true, "zoomToFitOnOpen": true, "zoomToFitOnResize": true, "zoomToFitMaxLevel": 2, @@ -79,7 +79,7 @@ "iframelyAllowed": true, "pngExportScale": 1, "exportWithTheme": true, - "exportWithBackground": true, + "exportWithBackground": false, "exportPaddingSVG": 10, "exportEmbedScene": false, "keepInSync": true, diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 2efa7c0..d3a2aa6 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -4,33 +4,21 @@ "type": "split", "children": [ { - "id": "a571fbe4f002d1e6", + "id": "e8c70b35b95d6458", "type": "tabs", "children": [ { - "id": "65449c74cd8d0f53", + "id": "88216c46794d50ee", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "Física/Cinematica.md", + "file": "Matematicas/Números complejos.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "Cinematica" - } - }, - { - "id": "5dd4b4bb82605fc9", - "type": "leaf", - "state": { - "type": "excalidraw", - "state": { - "file": "Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md" - }, - "icon": "excalidraw-icon", - "title": "Cinematica 09-09-25_09.excalidraw" + "title": "Números complejos" } } ] @@ -182,54 +170,53 @@ "obsidian-excalidraw-plugin:New drawing": false } }, - "active": "65449c74cd8d0f53", + "active": "88216c46794d50ee", "lastOpenFiles": [ - "Pasted image 20250909095158.png", + "Apuntes.md", + "Matematicas/Números complejos.md", + "Ilustraciónes/Números complejos 09-09-25_11_1.excalidraw.md", + "Ilustraciónes/Números complejos 09-09-25_11_1.excalidraw.svg", + "Ilustraciónes/Números complejos 09-09-25_10_1.excalidraw.md", + "Ilustraciónes/Números complejos 09-09-25_11_0.excalidraw.md", + "Ilustraciónes/Números complejos 09-09-25_11_0.excalidraw.svg", + "Ilustraciónes/Números complejos 09-09-25_11.excalidraw.md", + "Ilustraciónes/Números complejos 09-09-25_11.excalidraw.svg", + "Ilustraciónes/Números complejos 09-09-25_10_1.excalidraw.svg", + "Ilustraciónes/Números complejos 09-09-25_10_0.excalidraw.md", + "Ilustraciónes/Números complejos 09-09-25_10_0.excalidraw.svg", + "Ilustraciónes/Mates 09-09-25_10_0.excalidraw.svg", + "Ilustraciónes/Números complejos 09-09-25_10.excalidraw.md", + "Ilustraciónes/Números complejos 09-09-25_10.excalidraw.svg", + "Ilustraciónes/Mates 09-09-25_10_0.excalidraw.md", + "Ilustraciónes/Mates 09-09-25_10.excalidraw.svg", "Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md", + "Ilustraciónes/Mates 09-09-25_10.excalidraw.md", + "Ilustraciónes/img_09-09-25_10.excalidraw.md", + "Ilustraciónes/img_09-09-25_10.excalidraw.svg", "Física/Cinematica.md", - "Ilustraciónes/Cinematica 09-09-25_09.excalidraw.svg", + "Matematicas", + "Resources/Pasted image 20250909095158.png", "Física/Física.md", "Química/Introducción Química.md", - "Apuntes.md", "Física", "Introducción Quimica/Sustancias Inorgánicas.md", - "Introducción Quimica/Contenido/TablaPeriódica.png", - "Introducción Quimica/Contenido/TablaPeriódicaNO.webp", "Introducción Quimica/Contenido/TablaPeriódica2.pdf", "Introducción Quimica/Estequiometría de las reacciones químicas.md", "Resources", - "Resources/Pasted image 20250908122619.png", "Ilustraciónes/img_04-09-25_09_0.excalidraw.md", "Química", "Ilustraciónes/img_04-09-25_09.excalidraw.md", "Ilustraciónes/Estequiometría de las reacciones químicas 04-09-25_09.excalidraw.md", - "Ilustraciónes/img_04-09-25_09_0.excalidraw.svg", - "Ilustraciónes/Estequiometría de las reacciones químicas 04-09-25_09.excalidraw.svg", - "Ilustraciónes/img_04-09-25_09.excalidraw.svg", "Introducción Quimica/Introducción Química.md", "Introducción Quimica/Sustancias orgánicas.md", "Ilustraciónes/img_03-09-25_12.excalidraw.md", "School", - "Ilustraciónes/img_03-09-25_12.excalidraw.svg", "Ilustraciónes/Drawing 2025-09-03 09.16.17.excalidraw.md", "Introducción Quimica/Contenido/Contenido.md", - "Ilustraciónes/Drawing 2025-09-03 09.16.17.excalidraw.svg", "Untitled.canvas", - "Ilustraciónes/Drawing 2025-09-02 09.39.04.excalidraw.md", - "Ilustraciónes/Drawing 2025-09-02 09.39.04.excalidraw.svg", - "Perlite/SECURITY.md", - "Perlite/README.md", - "Perlite/Changelog.md", - "Introducción Quimica/Drawing 2025-09-02 10.13.03.excalidraw.md", - "Introducción Quimica/Drawing 2025-09-02 10.01.02.excalidraw.md", - "Ilustraciónes/Drawing 2025-09-02 09.35.04.excalidraw.md", "Introducción Quimica/Contenido", "Perlite/web/conf.d/default.conf", "Perlite/web/conf.d", - "Introducción Quimica/Enlaces.md", - "Introducción Quimica/Composición de materiales.md", - "Introducción Quimica/Elementos y átomos.md", - "docker-compose.yml", - "Perlite/web/config/default.conf" + "docker-compose.yml" ] } \ No newline at end of file diff --git a/Apuntes.md b/Apuntes.md index bba2b49..836fd54 100644 --- a/Apuntes.md +++ b/Apuntes.md @@ -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]] diff --git a/Física/Cinematica.md b/Física/Cinematica.md index 661190c..3674060 100644 --- a/Física/Cinematica.md +++ b/Física/Cinematica.md @@ -32,7 +32,7 @@ $$ # Aceleración constante -![[../Pasted image 20250909095158.png]] +![[../Resources/Pasted image 20250909095158.png]] # Movimiento Circular - Coordenadas cartesianas (x, y) diff --git a/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md b/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md index 9eebf41..ccc38d5 100644 --- a/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md +++ b/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.md @@ -41,7 +41,7 @@ tags: [excalidraw] "version": 13, "versionNonce": 1767061523, "isDeleted": false, - "boundElements": null, + "boundElements": [], "updated": 1757403083918, "link": null, "locked": false, @@ -110,10 +110,7 @@ tags: [excalidraw] 0 ], "simulatePressure": false, - "lastCommittedPoint": [ - 340, - -211 - ] + "lastCommittedPoint": null }, { "id": "bwpMviuGTGm-qt_-qlTsj", @@ -138,7 +135,7 @@ tags: [excalidraw] "version": 16, "versionNonce": 1844038739, "isDeleted": false, - "boundElements": null, + "boundElements": [], "updated": 1757403085036, "link": null, "locked": false, @@ -222,10 +219,7 @@ tags: [excalidraw] 0 ], "simulatePressure": false, - "lastCommittedPoint": [ - 312, - 105 - ] + "lastCommittedPoint": null }, { "id": "5WlaBGFRpMl2qCGpiZwHK", @@ -250,7 +244,7 @@ tags: [excalidraw] "version": 32, "versionNonce": 347760243, "isDeleted": false, - "boundElements": null, + "boundElements": [], "updated": 1757403091330, "link": null, "locked": false, @@ -414,10 +408,7 @@ tags: [excalidraw] 0 ], "simulatePressure": false, - "lastCommittedPoint": [ - 38, - -334 - ] + "lastCommittedPoint": null }, { "id": "8OGSja4qF_6X5U-zrw-fk", @@ -442,7 +433,7 @@ tags: [excalidraw] "version": 3, "versionNonce": 1966483485, "isDeleted": false, - "boundElements": null, + "boundElements": [], "updated": 1757403099211, "link": null, "locked": false, @@ -458,9 +449,78 @@ tags: [excalidraw] ], "pressures": [], "simulatePressure": true, + "lastCommittedPoint": null + }, + { + "id": "LCc0QBNue7zr1QcqoiNSu", + "type": "freedraw", + "x": -88, + "y": -290.2578125, + "width": 28, + "height": 155, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 0.5, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "index": "a9", + "roundness": null, + "seed": 1884817163, + "version": 10, + "versionNonce": 505102379, + "isDeleted": false, + "boundElements": null, + "updated": 1757405646380, + "link": null, + "locked": false, + "points": [ + [ + 0, + 0 + ], + [ + -1, + 118 + ], + [ + 16, + 145 + ], + [ + 27, + 155 + ], + [ + 8.479099281942695, + 125.80079287090444 + ], + [ + 3.2022833830136506, + 126.38710574856322 + ], + [ + 2.6159705053548237, + 127.55973150388078 + ], + [ + 2.6159705053548237, + 130.4912958921747 + ], + [ + 2.6159705053548237, + 130.4912958921747 + ] + ], + "pressures": [], + "simulatePressure": true, "lastCommittedPoint": [ - 0.0001, - 0.0001 + 2.6159705053548237, + 130.4912958921747 ] } ], @@ -481,10 +541,10 @@ tags: [excalidraw] "currentItemEndArrowhead": "arrow", "currentItemArrowType": "round", "currentItemFrameRole": null, - "scrollX": 837, - "scrollY": 484.7421875, + "scrollX": 549.7438286004008, + "scrollY": 373.46839937573804, "zoom": { - "value": 1 + "value": 1.705574 }, "currentItemRoundness": "round", "gridSize": 20, diff --git a/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.svg b/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.svg index a75a2f3..75fe993 100644 --- a/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.svg +++ b/Ilustraciónes/Cinematica 09-09-25_09.excalidraw.svg @@ -1,2 +1,2 @@ \ No newline at end of file + \ No newline at end of file diff --git a/Ilustraciónes/Mates 09-09-25_10.excalidraw.md b/Ilustraciónes/Mates 09-09-25_10.excalidraw.md new file mode 100644 index 0000000..036216e --- /dev/null +++ b/Ilustraciónes/Mates 09-09-25_10.excalidraw.md @@ -0,0 +1,261 @@ +--- + +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 +{ + "type": "excalidraw", + "version": 2, + "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.15.1", + "elements": [ + { + "id": "XaWnzw_pGySdUTirb4P6H", + "type": "freedraw", + "x": -81, + "y": -145.2578125, + "width": 259, + "height": 273, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "index": "a0", + "roundness": null, + "seed": 2093749637, + "version": 39, + "versionNonce": 154753835, + "isDeleted": false, + "boundElements": null, + "updated": 1757405630768, + "link": null, + "locked": false, + "points": [ + [ + 0, + 0 + ], + [ + 10, + 13 + ], + [ + 22, + 25 + ], + [ + 52, + 44 + ], + [ + 108, + 63 + ], + [ + 124, + 66 + ], + [ + 148, + 67 + ], + [ + 154, + 68 + ], + [ + 140, + 81 + ], + [ + 126, + 93 + ], + [ + 75, + 123 + ], + [ + 0, + 168 + ], + [ + -71, + 222 + ], + [ + -103, + 250 + ], + [ + -105, + 251 + ], + [ + -96, + 248 + ], + [ + -66, + 229 + ], + [ + -18, + 195 + ], + [ + 47, + 140 + ], + [ + 60, + 121 + ], + [ + 75, + 70 + ], + [ + 69, + 54 + ], + [ + 45, + 35 + ], + [ + 27, + 30 + ], + [ + -11, + 42 + ], + [ + -24, + 62 + ], + [ + -40, + 85 + ], + [ + -39, + 89 + ], + [ + -24, + 89 + ], + [ + -3, + 77 + ], + [ + 23, + 49 + ], + [ + 44, + 14 + ], + [ + 48, + -9 + ], + [ + 42, + -22 + ], + [ + 26, + -15 + ], + [ + 1, + 5 + ], + [ + -12, + 24 + ], + [ + -12, + 24 + ] + ], + "pressures": [], + "simulatePressure": true, + "lastCommittedPoint": [ + -12, + 24 + ] + } + ], + "appState": { + "theme": "dark", + "viewBackgroundColor": "#ffffff", + "currentItemStrokeColor": "#1e1e1e", + "currentItemBackgroundColor": "transparent", + "currentItemFillStyle": "solid", + "currentItemStrokeWidth": 2, + "currentItemStrokeStyle": "solid", + "currentItemRoughness": 1, + "currentItemOpacity": 100, + "currentItemFontFamily": 5, + "currentItemFontSize": 20, + "currentItemTextAlign": "left", + "currentItemStartArrowhead": null, + "currentItemEndArrowhead": "arrow", + "currentItemArrowType": "round", + "currentItemFrameRole": null, + "scrollX": 837, + "scrollY": 484.7421875, + "zoom": { + "value": 1 + }, + "currentItemRoundness": "round", + "gridSize": 20, + "gridStep": 5, + "gridModeEnabled": false, + "gridColor": { + "Bold": "rgba(217, 217, 217, 0.5)", + "Regular": "rgba(230, 230, 230, 0.5)" + }, + "currentStrokeOptions": null, + "frameRendering": { + "enabled": true, + "clip": true, + "name": true, + "outline": true, + "markerName": true, + "markerEnabled": true + }, + "objectsSnapModeEnabled": false, + "activeTool": { + "type": "freedraw", + "customType": null, + "locked": false, + "fromSelection": false, + "lastActiveTool": null + } + }, + "files": {} +} +``` +%% \ No newline at end of file diff --git a/Ilustraciónes/Mates 09-09-25_10.excalidraw.svg b/Ilustraciónes/Mates 09-09-25_10.excalidraw.svg new file mode 100644 index 0000000..59ee9bf --- /dev/null +++ b/Ilustraciónes/Mates 09-09-25_10.excalidraw.svg @@ -0,0 +1,2 @@ + \ No newline at end of file diff --git a/Ilustraciónes/Mates 09-09-25_10_0.excalidraw.md b/Ilustraciónes/Mates 09-09-25_10_0.excalidraw.md new file mode 100644 index 0000000..bd3fa8b --- /dev/null +++ b/Ilustraciónes/Mates 09-09-25_10_0.excalidraw.md @@ -0,0 +1,444 @@ +--- + +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 +{ + "type": "excalidraw", + "version": 2, + "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.15.1", + "elements": [ + { + "id": "qQ5byfvF2MnlMfM6CpLAV", + "type": "freedraw", + "x": -121, + "y": -184.2578125, + "width": 166, + "height": 195, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "index": "a0", + "roundness": null, + "seed": 467890539, + "version": 31, + "versionNonce": 938522981, + "isDeleted": false, + "boundElements": [], + "updated": 1757405713987, + "link": null, + "locked": false, + "points": [ + [ + 0, + 0 + ], + [ + -4, + 12 + ], + [ + -4, + 15 + ], + [ + -4, + 19 + ], + [ + 2, + 29 + ], + [ + 11, + 35 + ], + [ + 42, + 29 + ], + [ + 60, + 15 + 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"opacity": 100, + "groupIds": [], + "frameId": null, + "index": "a2", + "roundness": null, + "seed": 767138501, + "version": 16, + "versionNonce": 1326368197, + "isDeleted": false, + "boundElements": [], + "updated": 1757405715803, + "link": null, + "locked": false, + "points": [ + [ + 0, + 0 + ], + [ + -13, + 29 + ], + [ + -16, + 36 + ], + [ + -16, + 42 + ], + [ + -17, + 69 + ], + [ + -18, + 83 + ], + [ + -9, + 102 + ], + [ + 8, + 122 + ], + [ + 33, + 133 + ], + [ + 56, + 133 + ], + [ + 71, + 125 + ], + [ + 80, + 115 + ], + [ + 83, + 113 + ], + [ + 83, + 112 + ], + [ + 83, + 112 + ] + ], + "pressures": [], + "simulatePressure": true, + "lastCommittedPoint": null + } + ], + "appState": { + "theme": "dark", + "viewBackgroundColor": "transparent", + "currentItemStrokeColor": "#1e1e1e", + "currentItemBackgroundColor": "transparent", + "currentItemFillStyle": "solid", + "currentItemStrokeWidth": 2, + "currentItemStrokeStyle": "solid", + "currentItemRoughness": 1, + "currentItemOpacity": 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b/Ilustraciónes/Mates 09-09-25_10_0.excalidraw.svg new file mode 100644 index 0000000..475824f --- /dev/null +++ b/Ilustraciónes/Mates 09-09-25_10_0.excalidraw.svg @@ -0,0 +1,2 @@ + \ No newline at end of file diff --git a/Ilustraciónes/Números complejos 09-09-25_10.excalidraw.md b/Ilustraciónes/Números complejos 09-09-25_10.excalidraw.md new file mode 100644 index 0000000..fe8c4ee --- /dev/null +++ b/Ilustraciónes/Números complejos 09-09-25_10.excalidraw.md @@ -0,0 +1,5783 @@ +--- + +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'. 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09-09-25_10_0.excalidraw.md new file mode 100644 index 0000000..311e923 --- /dev/null +++ b/Ilustraciónes/Números complejos 09-09-25_10_0.excalidraw.md @@ -0,0 +1,11536 @@ +--- + +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'. 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09-09-25_10_1.excalidraw.svg b/Ilustraciónes/Números complejos 09-09-25_10_1.excalidraw.svg new file mode 100644 index 0000000..3cee4c8 --- /dev/null +++ b/Ilustraciónes/Números complejos 09-09-25_10_1.excalidraw.svg @@ -0,0 +1,2 @@ + \ No newline at end of file diff --git a/Ilustraciónes/Números complejos 09-09-25_11.excalidraw.md b/Ilustraciónes/Números complejos 09-09-25_11.excalidraw.md new file mode 100644 index 0000000..1e2937d --- /dev/null +++ b/Ilustraciónes/Números complejos 09-09-25_11.excalidraw.md @@ -0,0 +1,1752 @@ +--- + +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'. 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09-09-25_11_0.excalidraw.md new file mode 100644 index 0000000..843ceeb --- /dev/null +++ b/Ilustraciónes/Números complejos 09-09-25_11_0.excalidraw.md @@ -0,0 +1,12440 @@ +--- + +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'. 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b/Matematicas/Números complejos.md new file mode 100644 index 0000000..9211659 --- /dev/null +++ b/Matematicas/Números complejos.md @@ -0,0 +1,55 @@ +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 $r'^{\mu}=r$ $\mu\alpha'=\alpha(+k2\pi)$ \ No newline at end of file diff --git a/Pasted image 20250909095158.png b/Resources/Pasted image 20250909095158.png similarity index 100% rename from Pasted image 20250909095158.png rename to Resources/Pasted image 20250909095158.png