Simplify the following expression.

Question

left-parenthesis negative 4 plus 2 i right-parenthesis divided by left-parenthesis 1 plus i right-parenthesis
(1 point)
Responses

1 minus i
Image with alt text: 1 minus i

3 minus i
Image with alt text: 3 minus i

2 minus 2 i
Image with alt text: 2 minus 2 i

6 minus 2 i

Answer 1

To simplify the expression

(-4 + 2i) / (1 + i),

you can multiply the numerator and denominator by the conjugate of the denominator, which is (1 - i):

((-4 + 2i) / (1 + i)) * ((1 - i) / (1 - i))

Simplifying this expression further gives:

((-4 + 2i)(1 - i)) / ((1 + i)(1 - i))

= ((-4 + 4i - 2i - 2i^2)) / (1 - i^2)

Since i^2 equals -1, we can substitute its value:

= (-4 + 6i - 2(-1)) / (1 - (-1))

= (-4 + 6i + 2) / (1 + 1)

= (-2 + 6i) / 2

= -1 + 3i.

Therefore, the simplified expression is -1 + 3i.