Respuesta :

mhanifa

Answer:

Use identities:

  • (a + b)² = a² + 2ab + b²
  • i² = -1

Simplify:

  • (x + (3 + 5i))² =
  • x² + 2x(3 + 5i) + (3 + 5i)² =
  • x² + 6x + 10xi + 9 + 30i - 25 =
  • x² + 6x + 10xi + 30i - 16

Identity used:-

[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]

Now

[tex]\\ \sf\longmapsto (x+(3+5i))^2[/tex]

[tex]\\ \sf\longmapsto x^2+2x(3+5i)+(3+5i)^2[/tex]

[tex]\\ \sf\longmapsto x^2+6x+10xi+3^2+2(3)(5i)+(5i)^2[/tex]

  • i^2=-1

[tex]\\ \sf\longmapsto x^2+6x+10xi+9+30i-25[/tex]

[tex]\\ \sf\longmapsto x^2+6x+10xi+30i+9-25[/tex]

[tex]\\ \sf\longmapsto x^2+6x+10xi+30i-16[/tex]

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