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CLASE 10

CLASE 10. DIVISIÓN DE NÚMEROS COMPLEJOS.  3  3. 5 3 3. 5  3. 5  3. 5 3 (  3). =. =. 2. 22 4+  5. 22 4+  5. 22(4–  5). =2(4–  5). 22(4–  5). 22(4–  5). 4–  5 4–  5. =. =. 2. 2. 16–5. ( 4 ) – (  5 ). 11.

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CLASE 10

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  1. CLASE 10

  2. DIVISIÓN DE NÚMEROS COMPLEJOS

  3. . 3 3 53 3 5 3 5 3 53 (3) = = 2 22 4+5 22 4+5 22(4–5) =2(4–5) 22(4–5) 22(4–5) . 4–5 4–5 = = 2 2 16–5 (4) –(5) 11 Racionaliza los denominadores: a) = = b) = . Expresiones conjugadas

  4. a+bi a–bi . CONJUGADOS + . 0,8–4i2 0,8+4i2 . 2 = 9–16i 2 2 . (3) –(4i ) = Números complejos producto –7+2i –7–2i 3 – 4i 3 + 4i . 3–4i 3+4i + = 9 +16 = 25 = 9–16(–1)

  5. 5 2 5+4i –2 + = = 2i Efectúa: 5 4i –2 –2 .

  6. Efectúa: –1 –1 . = 2–i –1–2i 2–i –1–2i –1+2i –1+2i 2 –2+4i+i –2i = = 2 2 1 – (2 i ) 2 2 (–1) –(2i ) = = = 2 1 – 4i –2 + 5i + 2 . 5i 5i 5i = i 1 + 4 5

  7. En la práctica, para dividir dos números complejos en forma binómica procedemos a multiplicar el dividendo y el divisor por el número conjugado del divisor.

  8. 3 – i 1 – i 3 3 – i 2 i ESTUDIO INDIVIDUAL Calcula: .

  9. 2 –1 1 = 2–i –1–2i 2 4 – 4i + i = = = 2 1 + 4i + 4i = i –3–4i 2 2 =1 + 4i + 4i 2 = · = ( ) –(1+2i ) –3–4i = = = 9–16i (–3)2–(4i)2 2 Efectúa: (2–i )2 4–4i –1 1+4i –4 (–1–2i )2 (3–4i ) (–1) (3+4i ) 3–4i –3+4i 9 +16 (–1) (9 +16) (–1–2i )2 . = –1 25

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