Can someone help me simplify the expression (6+6i)-(2+i)

Question

anonymous · Answer

The choices are 
a. 4i
b. 4i+4
c. 4+5i
d. 9i

mathstudent55 · Answer

First, drop the first set of parentheses since they are not needed.

anonymous · Answer

6+6i-(2+i)

anonymous · Answer

it would be 4+5i right?

mathstudent55 · Answer

(6 + 6i) - (2 + i) =
= 6 + 6i - (2 + i)

Good, you got it.
Now you have a negative sign outside the remaining set of parentheses.
That is the same as having a -1 there. See below:

= 6 + 6i - 1(2 + i)

You need to distribute the -1 by the parentheses. You multiply each term inside the parentheses by -1. What that ends up doing is changing each sign inside the parentheses.

= 6 + 6i - 2 - i

Ok so far?

anonymous · Answer

Yeah I got it!  I understand this one. @mathstudent55

mathstudent55 · Answer

Now just collect like terms.
Add 6 and -2
Add 6i and -1

mathstudent55 · Answer

= 6 + 6i - 2 - i

= 4 + 5i