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CLASE 17

CLASE 17. EJERCITACIÓN VARIADA. OPERACIONES Y ECUACIONES EN. C. i es la unidad imaginaria. i. 1 2. •. C. 2. • i. R. 1 es la unidad real. • i. • 2+  i. • 1. • . • 0. • 1 + i. = – 1. • –0,3 + 5 i. Halla, si existen, todas las x  R. que satisfacen la igualdad:.

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CLASE 17

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  1. CLASE 17

  2. EJERCITACIÓN VARIADA. OPERACIONES Y ECUACIONES EN C

  3. i es la unidad imaginaria i 1 2 • C 2 •i R 1 es la unidad real •i •2+i •1 •  • 0 •1 + i = –1 •–0,3 + 5i .

  4. Halla, si existen, todas las xR que satisfacen la igualdad: x2–3x x2–3x x+ 2 1 x–3 1 x–3 +16i = 5 + 2 i x+ · x2–3x 4 = 2 2 (x–3) · : 16 5 = = x(x–3)+1=5(x–3) x2–3x+1=5x–15 4 = x2–3x x2–3x+1–5x+15=0 0 = x2–3x–4 x2–8x+16=0

  5. 0 = x2–3x–4 x2–8x+16 = 0 (x – 4)2=0 0 = (x – 4)(x + 1) x – 4=0 ó x + 1=0 x – 4 = 0 x = 4 ó x = –1 x = 4 El único número real x que satisface la igualdad es 4 . .

  6. Resuelve la siguiente ecuación en el conjunto de los números complejos: · x x4+ = x3+16 16 x x0 x5+16 = x4+16x : x5–x4–16x +16 = 0 x4(x – 1) 1 –1 0 0 –16 16 –16( )=0 x – 1 1 1 0 0 0 –16 (x – 1)(x4– 16) = 0 0 1 0 0 0 –16 (x – 1)(x2 – 4)(x2 + 4) = 0

  7. (x – 1)(x2 – 4)(x2+ 4) = 0 x=  4 x= –4 2 = 4i x– 1 = 0 x= 1 x = 1 x= 2 x2– 4 = 0 x = 2 x2 = 4 Cinco soluciones x =–2 x = 2i x = 2i x2+ 4 = 0 x =–2i x2 = –4 .

  8. C D= 16 x2+ 1 = 10 x ESTUDIO INDIVIDUAL a) Resuelve en el conjunto la ecuación: x=2 x=–1+2i x=–1–2i b) Determina los números reales x que satisfacen la igualdad: 2 log x+(x+2+x)i=log(x+2)+4i x=2 .

  9. . Efectúa: 4 . (2cis60o) cis90o 81 4 (1+i3 ) i . = = =1+3 8 cis150o =3  =(1) +(3) 2 2 = 1 4 81 3 1 = i = i 81 tan = 1+i3 i 8 cis150o 16 cis240o · cis90o 16 cis330o 8 cis150o 8 cis150o = –2 = 2 cis180o = 2 = cis 90o 20  = 60o 1

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