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
The simplified expression is 8 - 4i.
To simplify the expression (–2 – 2i)(–4 + 6i), you need to apply the distributive property.
Starting with the first term:
-2 multiplied by -4 is 8.
-2 multiplied by 6i is -12i.
Moving on to the second term:
-2i multiplied by -4 is 8i.
-2i multiplied by 6i is -12i².
Since i² is equal to -1, you can simplify -12i² to +12.
Combining the terms:
8 - 12i + 8i + 12 = 20 - 4i.
Therefore, the simplified expression is 20 - 4i.
To simplify the expression (–2 – 2i)(–4 + 6i), you can use the distributive property and combine like terms.
First, let's distribute –2 to both terms inside the parentheses:
–2 * –4 = 8
–2 * 6i = –12i
Next, let's distribute –2i to both terms inside the parentheses:
–2i * –4 = 8i
–2i * 6i = –12i^2
Now, let's simplify –12i^2. Since i represents the imaginary unit, i^2 is equal to –1. Therefore, –12i^2 becomes –12 * –1 = 12.
Now we can combine all the terms we obtained:
8 + 8i - 12i + 12
Combining like terms, we get:
(8 + 12) + (8i - 12i)
Simplifying further:
20 - 4i
Therefore, the simplified expression is 20 - 4i.