We want to simplify the expression:
\((x + (3+5i))^2 = (x + (3+5i))(x + (3+5i))\)
We will see that it is equivalent to:
\((x^2 + 6*x - 16) + (x*10 + 30)*i\)
Here we need to remember that:
i² = -1
With this in mind, we can simplify the given expression:
\((x + (3+5i))^2 = (x + (3+5i))(x + (3+5i))\\= x^2 + x*3 + x*5i + 3*x + 9 + 15i + (5i)*x + (5i)*3 + (5i)*(5i)\\= x^2 + 6*x + 9 - 25 + (x*10 + 30)*i\\= (x^2 + 6*x - 16) + (x*10 + 30)*i\)
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
