- El número real y complejo.
- Inecuaciones con valor absoluto.
- Los numeros complejos.
- Formula de Moivre.
- Límite, continuidad, derivabilidad de funciones reales de variable real.
- Fórmula de Taylor.
- Integración.
- Teorema fundamental del cálculo.
- Teorema del cambio de variab...
Existe una ordenación
𝑁 AX8 Orden total 𝑥 ≤ 𝑦 ∨ 𝑦 ≤ 𝑥 ∀𝑥, 𝑦
𝑁 AX9 𝑥 ≤ 𝑦; 𝑧 𝑥+𝑧≤𝑦+𝑧
𝑍 AX10 𝑥 ≤ 𝑦 ∧ 𝑧 ≥ 0 𝑥·𝑦≤𝑦·𝑧
𝑅 AX11 Axioma del extremo superior: todo conjunto acotado superiormente tiene un
extremo superior.
𝐴 está acotado superiormente si existe 𝑘cota superior. 𝑥 ≤ 𝑘 ∀𝑥 ∈ 𝐴
Extremo superior (si existe) es la menor de las cotas superiores αes extremo superior si es
cota superior y α ≤ 𝑘si 𝑘es cota superior.
Ejemplo que estando acotado no tiene extremo superior: 𝐴 = 𝑄 ∩ (0, 2)
207145−207
Cálculo de la fracción generatriz: 2, 07145 = 99900
Inecuaciones con valor absoluto.
|𝑥| = {𝑥 𝑠𝑖 𝑥 ≥ 0; − 𝑥 𝑠𝑖 𝑥 < 0}
2 2
𝑍 = 𝑎 + 𝑏𝑖; |𝑍| = 𝑎 + 𝑏
Llamamos argumento principal al ángulo que forma el vector complejo con respecto al eje
OX teniendo en cuenta que: − π ≤ θ ≤ π
𝑏 𝑏
θ = 𝑎𝑟𝑐𝑡𝑔 𝑎
θ = 𝑎𝑟𝑐𝑡𝑔 𝑎
+ π
𝑏 𝑏
θ = 𝑎𝑟𝑐𝑡𝑔 𝑎
− π θ = 𝑎𝑟𝑐𝑡𝑔 𝑎
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