simplify the following expressions involving complex numbers.

(3+2i)-(-7-i)

is i like x? and how would this work i know that you do this:
(3+2i)(7+i)
to get rid of the sign between the expressions.
but then what?

When simplifying expressions involving complex numbers, it's important to remember that the imaginary unit, represented by "i," follows the property: i^2 = -1.

Let's start with the expression: (3+2i) - (-7-i).

To simplify this, we can distribute the minus sign to both terms inside the parentheses:

(3 + 2i) - (-7 - i)
= 3 + 2i + 7 + i

Now we can combine like terms:

= (3 + 7) + (2i + i)
= 10 + 3i

Therefore, the simplified expression is 10 + 3i.

Now, let's address your question about simplifying the expression (3+2i)(7+i).

To simplify this expression, we use the distributive property of multiplication over addition. This means we multiply each term inside the first parentheses by each term inside the second parentheses:

(3 + 2i)(7 + i)
= 3(7) + 3(i) + 2i(7) + 2i(i)

Now, let's simplify each term:

= 21 + 3i + 14i + 2i^2

Remember, i^2 = -1, so we can substitute it into the expression:

= 21 + 3i + 14i + 2(-1)

Next, simplify further:

= 21 + 3i + 14i - 2
= 19 + 17i

Therefore, the simplified expression is 19 + 17i.