Ejercicio 254

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CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 254
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  1. 4 + 16 = (1 ) ( 2 2 ) + (1 ) ( 4 2 ) =2 1 +4 1 =2i+4i =6i
  2. 25 + 81 49 = (1 ) ( 5 2 ) + (1 ) ( 9 2 ) (1 ) ( 7 2 ) =5 1 +9 1 7 1 =5i+9i7i =7i
  3. 2 9 +3 100 =2 (1 ) ( 3 2 ) +3 (1 ) (1 0 2 ) =2.3 1 +3.10 1 =6i+30i =36i
  4. 3 64 5 49 +3 121 =3 (1 ) ( 8 2 ) 5 (1 ) ( 7 2 ) +3 (1 ) ( 11 ) 2 =3.8 1 5.7 1 +3.11 1 =24i35i+33i =22i
  5. 2 a 2 + a 4 + a 6 =2 (1 ) ( a 2 ) + (1 ) ( a 4 ) + (1 ) ( a 6 ) =2a 1 + a 2 1 + a 3 1 =2ai+ a 2 i+ a 3 i =i(2a+ a 2 + a 3 )
  6. 18 + 8 +2 50 = (1 ) ( 2 ) ( 3 2 ) + (1 ) ( 2 ) ( 2 2 ) +2 (1 ) ( 2 ) ( 5 2 ) =3 1 2 +2 1 2 +2.5 1 2 =3 2 i+2 2 i+10 2 i =15 2 i
  7. 3 20 2 45 +3 125 =3 (1 ) ( 5 ) ( 2 2 ) 2 (1 ) ( 5 ) ( 3 2 ) +3 (1 ) ( 5 ) ( 5 2 ) =3.2 5 1 2.3 5 1 +3.5 5 1 = 6 5 i 6 5 i +15 5 i =15 5 i
  8. a 4 +4 9 a 4 3 4 a 4 = (1 ) ( a 4 ) +4 (1 ) ( 3 2 ) ( a 4 ) 3 (1 ) ( 2 2 ) ( a 4 ) = a 2 1 +4.3 a 2 1 3.2 a 2 1 = a 2 i+12 a 2 i6 a 2 i =7 a 2 i