Respuesta :

(x + (3 + 5i))*(x + (3+5i))
= x^2 + x(3+5i) + x(3+5i) + (3 + 5i)^2
= x^2 + 2x(3+5i) + 9 + 6(5i) + 25i^2
= x^2 + 6x +10xi + 9 + 30i - 25
= x^2 + 6x + 10xi + 30i - 16
facundo3141592

We want to simplify the expression:

[tex](x + (3+5i))^2 = (x + (3+5i))(x + (3+5i))[/tex]

We will see that it is equivalent to:

[tex](x^2 + 6*x - 16) + (x*10 + 30)*i[/tex]

Here we need to remember that:

i² = -1

With this in mind, we can simplify the given expression:

[tex](x + (3+5i))^2 = (x + (3+5i))(x + (3+5i))\\= x^2 + x*3 + x*5i + 3*x + 9 + 15i + (5i)*x + (5i)*3 + (5i)*(5i)\\= x^2 + 6*x + 9 - 25 + (x*10 + 30)*i\\= (x^2 + 6*x - 16) + (x*10 + 30)*i[/tex]

Where it is separated it in real part (first parenthesis) and complex part (second parenthesis)

If you want to learn more, you can read:

https://brainly.com/question/17203594

Otras preguntas