Question

Simplify. Express your answer in the form a + bi. (2+ i)(3 − 2i)−(i + 1)

Answer 1

You can just distribute the first part. I'm going to use the classic FOIL method, just like you might do for factors of a quadratic or other polynomial.

Let's look at this.
(2+i)(3-2i)
first: 2*3=6
outside: 2*-2i=-4i
inside: i*3=3i
last: i*-2i=-2i^2=2
6-4i+3i+2
8-i

Now, we can subtract.
(8-i)-(i+1)
8-i-i-1
7-2i

Answer 2

i dont understand this step
last: i*-2i=-2i^2=2

Answer 3

2i^2 = 2 ? how ?