Ejercicio 264

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Para graficar este grupo de ejercicios, se utilizara el software matemático Geogebra 6, el cual es un programa multiplataforma y cada ejercicio tendrá un link para la descarga del mismo realizado en Geogebra 6.
Ejercicio 264
Representar gráficamente:
  1. 2+2 1
    punto imaginario
  2. 2+3 1
    numero imaginario
  3. 45 1
    representacion de numero imaginario
  4. 73 1
    puntos imaginarios
  5. 1+i
    representacion punto imaginario
  6. 15i
    -i
  7. 36i
    recta imaginaria
  8. 5+4i
    puntos imaginarios
  9. 4 1 2 7 1
    punto imaginario 9
  10. 5 3 4 +6 1
    punto imaginario 10
  11. 1 1 2 2 1
    punto imaginario 9
  12. 1010i
    punto imaginario 12

Ejercicio 263

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 263
Dividir:
  1. (1+ 1 ) ÷ (1 1 ) 1+ 1 1 1 = 1+ 1 1 1 × 1+ 1 1+ 1 = (1+ 1 ) 2 1 2 ( 1 ) 2 = 1+2 1 + ( 1 ) 2 1(1 ) = 1 +2 1 1 1+1 = 2 1 2 =i
  2. (3+ 1 ) ÷ (3 1 ) = 3+ 1 3 1 × 3+ 1 3+ 1 = (3+ 1 ) 2 3 2 ( 1 ) 2 = 9+6 1 + ( 1 ) 2 9(1 ) = 9+6 1 1 9+1 = 8+6 1 10 = 2 (4+3i ) = 4+3i 5
  3. (53 1 ) ÷ (3+4 1 ) = 53 1 3+4 1 × 34 1 34 1 = (53i ) (34i ) 3 2 (4i ) 2 = 1520i9i+12 i 2 916 i 2 = 1529i+12(1 ) 916(1 ) = 1529i12 9+16 = 329i 25
  4. (85i ) ÷ (7+6i ) = 85i 7+6i × 76i 76i = (85i ) (76i ) 7 2 (6i ) 2 = 5648i35i+30 i 2 4936 i 2 = 5683i+30(1 ) 4936(1 ) = 5683i30 49+36 = 2683i 85
  5. (4+ 3 ) ÷ (54 3 ) = 4+ 3 54 3 × 5+4 3 5+4 3 = (4+ 3 i ) (5+4 3 i ) 5 2 (4 3 ) 2 = 20+16 3 i+5 3 i+4(3 i 2 ) 2516(3 ) = 20+21 3 i+12 i 2 25+48 = 20+21 3 i+12(1 ) 73 = 20+21 3 i12 73 = 8+21 3 i 73
  6. ( 2 +2 5 ) ÷ (4 2 5 ) = 2 +2 5 4 2 5 × 4 2 + 5 4 2 + 5 = 2 +2 5 i 4 2 5 i × 4 2 + 5 i 4 2 + 5 i = ( 2 +2 5 i ) (4 2 + 5 i ) (4 2 ) 2 ( 5 i ) 2 = 4( 2 ) + 10 i+8 10 i+2( 5 ) i 2 16( 2 ) 5 i 2 = 8+9 10 i+10(1 ) 325(1 ) = 8+9 10 i10 32+5 = 2+9 10 i 37

Ejercicio 262

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 262
  1. 1ipor1+i (1i ) (1+i ) = 1 2 i 2 =1(1 ) =1+1 =2
  2. 3+2 1 por32 1 (3+2 1 ) (32 1 ) = 3 2 (2 1 ) 2 =94(1 ) =9+4 =13
  3. 2 5ipor 2 +5i ( 2 5i ) ( 2 +5i ) = (2 ) 2 (5i ) 2 =225 i 2 =225(1 ) =2+25 =27
  4. 2 3 +4ipor2 3 4i (2 3 +4i ) (2 3 4i ) = (2 3 ) 2 (4i ) 2 =4( 3 ) 16 i 2 =1216(1 ) =12+16 =28
  5. 5 2 por5+ 2 (5 2 ) (5 2 ) = 5 2 ( 2 ) 2 =25(2 ) =25+2 =27
  6. 9 5 por9+ 5 (9 5 ) (9+ 5 ) = (9 ) 2 ( 5 ) 2 =81(5 ) =81+5 =86

Ejercicio 260

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 260
  1. De2 1 restar2+ 1 32 1 (5+3 1 ) =32i53i =25i
  2. De7+3 1 restar73 1 7+3 1 (73 1 ) = 7 +3 1 7 +3 1 =3i+3i =6i
  3. De37 1 restar3+7 1 37 1 (3+7 1 ) = 3 7 1 + 3 7 1 =7i7i =14i
  4. Restar5 2 de5+ 2 5+ 2 (5 2 ) = 5 2 + 5 + 2 = 1 2 + 1 2 = 2 i+ 2 i =2 2 i
  5. Restar 2 3 de 2 + 3 2 + 3 ( 2 3 ) = 2 + 3 2 + 3 = 1 3 + 1 3 = 3 i+ 3 i =2 3 i
  6. Restar 5 +4 2 de 5 4 2 5 4 2 ( 5 +4 2 ) = 5 4 2 + 5 4 2 =4 1 2 4 1 2 =4 2 i4 2 i =8 2 i

Ejercicio 259

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 259
Restar:
  1. De32 1 restar5+3 1 32 1 (5+3 1 ) =32i53i =25i
  2. De8+4 1 restar310 1 8+4 1 (310 1 ) =8+4i3+10i =5+14i
  3. De1 1 restar78 1 1 1 (78 1 ) =1i+7+8i =6+7i
  4. Restar53 1 de47 1 47 1 (53 1 ) =47i5+3i =14i
  5. Restar87 1 de154 1 154 1 (87 1 ) =154i8+7i =7+3i
  6. Restar350 1 de11+80 1 11+80 1 (350 1 ) =11+80i3+50i =8+130i
  7. De5 25 restar3+6i 5 25 (3+6i ) =5 25 36i =2 (1 ) ( 5 2 ) 6i =25 1 6i =25i6i =211i
  8. De4+ 5 restar2+ 3 4+ 5 (2+ 3 ) =4+ 5 2 3 =2+ (1 ) ( 5 ) (1 ) ( 3 ) =2+ 1 5 1 3 =2+ 5 i 3 i =2+( 5 3 ) i
  9. Restar 3 +6 1 de 2 5 1 2 5 1 ( 3 +6 1 ) = 2 5 1 3 6 1 = 2 5i 3 6i = 2 3 11i
  10. Restar7+ 3 de8 7 8 7 (7+ 3 ) =8 7 +7 3 =15 1 7 1 3 =15 7 i 3 i =15( 7 3 ) i

Ejercicio 258

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 258
Sumar:
  1. 72 1 ,7+2 1 7+2 1 +7+2 1 =7+2i+7+2i =14+4i
  2. 53 1 ,5+3 1 53 1 5+3 1 =5 3i 5+ 3i =10
  3. 9+i 3 ,9i 3 9+ i 3 +9 i 3 =18
  4. 75 1 ,7+5 1 75 1 7+5 1 =7 5i 7+ 5i =14
  5. 83 2 ,8+3 2 83 2 +8+3 2 =16 3 2 + 3 2 =16
  6. 2 +i 3 , 2 i 3 2 + i 3 + 2 i 3 =2 2

Ejercicio 257

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 257
Sumar:
  1. 2+3 1 ,52 1 2+3 1 +52 1 =2+3i+52i =7+i
  2. 45 1 ,2+8 1 45 1 2+8 1 =45i2+8i =6
  3. 1211 1 ,8+7 1 1211 1 +8+7 1 =1211i+8+7i =204i
  4. 5+ 1 ,7+2 1 ,9+7 1 5+ 1 +7+2 1 +9+7 1 =5+i+7+2i+9+7i =21+8i
  5. 32i,58i,10+13i 32i+58i10+13i =2+3i
  6. 1i,4+3i, 2 +5i 1i+4+3i+ 2 +5i = 2 +5+8i
  7. 2+ 2 ,4 3 2+ 2 +4 3 =2+ (1 ) ( 2 ) +4 (1 ) ( 3 ) =6+ 1 2 1 3 =6+ 2 i 3 i =6+( 2 3 ) i
  8. 7+ 5 , 2 9 ,4+ 16 7+ 5 + 2 9 4+ 16 =7+ (1 ) ( 5 ) + 2 (1 ) ( 3 2 ) 4+ (1 ) ( 4 2 ) =3+ 1 5 + 2 3 1 +4 1 =3+ 5 i+ 2 3i+4i =3+ 2 + 5 i+i =3+ 2 +( 5 +1 ) i

Ejercicio 256

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 256
Dividir:
  1. 16 ÷ 4 = 4 = 4 =2
  2. 10 ÷ 2 = 2 = 5
  3. 81 ÷ 3 = 3 = 27 = 3 3 =3 3
  4. 90 ÷ 5 = 5 = 18 = 2. 3 2 =3 2
  5. 150 ÷ 3 = 3 = 50 = 2. 5 2 =5 2
  6. 10 36 ÷ 5 4 = 5 4 =2 9 =2( 3 ) =6
  7. 2 18 ÷ 6 =2 6 =2 3
  8. 315 ÷ 7 = 7 = 45 = 5. 3 2 =3 5
  9. 27 4 ÷ 3 4 = 3 4 = 94 = 3 2 = 3
  10. 300 4 ÷ 12 4 = 12 4 = 254 = 5 2 = 5

Ejercicio 255

CAPITULO XXXII

CANTIDADES IMAGINARIAS
Ejercicio 255
Multiplicar
  1. 16 × 25 = (1 ) ( 4 2 ) × (1 ) ( 5 2 ) =4 1 × 5 (1 ) 5 =20 ( 1 ) 2 =20
  2. 81 × 49 = (1 ) ( 9 2 ) × (1 ) ( 7 2 ) =9 1 × 7 1 =63 ( 1 ) 2 =63
  3. 5 36 × 4 64 =5 (1 ) ( 6 2 ) × 4 (1 ) ( 8 2 ) =5 × 6 1 × 4 × 8 1 =960 ( 1 ) 2 =960
  4. 3 × 2 = (1 ) ( 3 ) × (1 ) ( 2 ) =3 1 × 2 1 =6 ( 1 ) 2 =6
  5. 2 5 × 3 7 =2 (1 ) ( 5 ) × 3 (1 ) ( 7 ) =2 1 5 × 3 1 7 =6 35 ( 1 ) 2 =6 35
  6. 3 × 75 = (1 ) ( 3 ) × (1 ) ( 3 ) ( 5 2 ) = 1 3 × 5 1 3 =5 ( 1 ) 2 (3 ) 2 =15
  7. 2 7 × 3 28 =2 (1 ) ( 7 ) × 3 (1 ) ( 2 2 ) ( 7 ) =2 1 7 × 3 × 2 1 7 =12 ( 1 ) 2 (7 ) 2 =84
  8. 49 × 4 × 9 = (1 ) ( 7 2 ) × (1 ) ( 2 2 ) × (1 ) ( 3 2 ) =7 1 × 2 1 × 3 1 =42 ( 1 ) 3 =42 ( 1 ) 2 ( 1 ) =42i
  9. 2 × 3 5 × 10 = (1 ) ( 2 ) × 3 (1 ) ( 5 ) × (1 ) ( 5 ) ( 2 ) = 1 2 × 3 1 5 × 1 5 2 =3 ( 1 ) 3 (5 ) 2 (2 ) 2 =3( 5 ) ( 2 ) ( 1 ) 2 ( 1 ) =30i
  10. 12 × 27 × 8 × 50 = (1 ) ( 2 2 ) ( 3 ) × (1 ) ( 3 2 ) ( 3 ) × (1 ) ( 2 2 ) ( 2 ) × (1 ) ( 5 2 ) ( 2 ) =2 1 3 × 3 1 3 × 2 1 2 × 5 1 2 =2 × 3 × 2 × 5 (3 ) 2 (2 ) 2 =60( 3 ) ( 2 ) =360
  11. 5 x × 3 y =5 (1 ) ( x ) × 3 (1 ) ( y ) =5 1 x × 3 1 y =15 ( 1 ) 2 xy =15 xy
  12. Mathematical Equation
  13. Mathematical Equation
  14. Mathematical Equation