Simplify the expression. (–2 – 2i)(–4 + 6i) (1 point) Responses 8 – 4i 8 – 4 i 8 – 12i 8 – 12 i 20 – 4i 20 – 4 i –4 – 4i –4 – 4 i
To simplify the expression (–2 – 2i)(–4 + 6i), we will use the distributive property.
The first term with the second term:
–2(-4) = 8
–2(6i) = –12i
The second term with the first term:
–2i(-4) = 8i
–2i(6i) = –12i^2
Simplifying further:
8 + 12i + 8i – 12i^2
Since i^2 is equal to –1:
8 + 12i + 8i – 12(-1)
8 + 12i + 8i + 12
Combining like terms:
20 + 20i
Therefore, the simplified expression is 20 + 20i.
To simplify the expression (–2 – 2i)(–4 + 6i), we will use the distributive property.
Step 1: Multiply the first terms of each binomial: -2 * -4 = 8
Step 2: Multiply the first term of the first binomial (-2) with the second term of the second binomial (6i): -2 * 6i = -12i
Step 3: Similarly, multiply the second term of the first binomial (-2i) with the first term of the second binomial (-4): -2i * -4 = 8i
Lastly, multiply the second terms of each binomial: -2i * 6i = -12i^2
Now, combine all the terms we obtained: 8 - 12i + 8i - 12i^2
Simplify -12i^2 by remembering that i^2 = -1: -12i^2 = -12 * -1 = 12
So, we have: 8 - 12i + 8i + 12
Combining like terms, we get: 20 - 4i
Thus, the simplified expression is 20 - 4i.
To simplify the expression (–2 – 2i)(–4 + 6i), you can use the distributive property of multiplication over addition.
First, multiply -2 by -4:
-2 * -4 = 8
Next, multiply -2 by 6i:
-2 * 6i = -12i
Then, multiply 2i by -4:
-2i * -4 = 8i
Lastly, multiply 2i by 6i:
-2i * 6i = -12i^2
Since i^2 is equal to -1, -12i^2 is equal to -12 * -1 = 12.
So, the final answer is 8 + 8i - 12 = -4 + 8i.
Therefore, the simplified expression is -4 + 8i.