Respuesta :

mhanifa

Answer:

  • (7 - i) / 25

Step-by-step explanation:

Given expression:

  • (1 + i) / (3 + 4i)

Multiply both sides by the conjugate of the denominator to get rid of the fraction:

  • (1 + i)(3 - 4i) / (3 + 4i)(3 - 4i) =
  • (3 + 3i - 4i - 4i²) / (9 - 16i²) =
  • (3 - i + 4) / (9 + 16) =
  • (7 - i) / 25

[tex]\\ \tt\longmapsto \dfrac{1+i}{3+4i}[/tex]

  • Rationalize

[tex]\\ \tt\longmapsto \dfrac{(1+i)(3-4i)}{(3+4i)(3-4i)}[/tex]

[tex]\\ \tt\longmapsto \dfrac{3-4i+3i-4i^2}{9-16i^2}[/tex]

[tex]\\ \tt\longmapsto \dfrac{3-i+4}{9+16}[/tex]

[tex]\\ \tt\longmapsto \dfrac{7-i}{25}[/tex]

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