Question
Multiply
(
5
−
10
i
)
(
−
3
+
8
i
)
(1 point)
(
5
−
10
i
)
(
−
3
+
8
i
)
(1 point)
Answers
Answered by
GPT-4o mini
To multiply the complex numbers \( (5 - 10i)(-3 + 8i) \), we can use the distributive property (also known as the FOIL method for binomials):
\[
(5 - 10i)(-3 + 8i) = 5 \cdot (-3) + 5 \cdot (8i) + (-10i) \cdot (-3) + (-10i) \cdot (8i)
\]
Now, we calculate each term:
1. \( 5 \cdot (-3) = -15 \)
2. \( 5 \cdot (8i) = 40i \)
3. \( (-10i) \cdot (-3) = 30i \)
4. \( (-10i) \cdot (8i) = -80i^2 \)
Since \( i^2 = -1 \), we substitute:
\[
-80i^2 = -80(-1) = 80
\]
Now, we combine all the terms:
\[
-15 + 40i + 30i + 80
\]
Next, we combine the like terms:
1. Real parts: \( -15 + 80 = 65 \)
2. Imaginary parts: \( 40i + 30i = 70i \)
Putting it all together, the result is:
\[
65 + 70i
\]
Thus, the product \( (5 - 10i)(-3 + 8i) \) is:
\[
\boxed{65 + 70i}
\]
\[
(5 - 10i)(-3 + 8i) = 5 \cdot (-3) + 5 \cdot (8i) + (-10i) \cdot (-3) + (-10i) \cdot (8i)
\]
Now, we calculate each term:
1. \( 5 \cdot (-3) = -15 \)
2. \( 5 \cdot (8i) = 40i \)
3. \( (-10i) \cdot (-3) = 30i \)
4. \( (-10i) \cdot (8i) = -80i^2 \)
Since \( i^2 = -1 \), we substitute:
\[
-80i^2 = -80(-1) = 80
\]
Now, we combine all the terms:
\[
-15 + 40i + 30i + 80
\]
Next, we combine the like terms:
1. Real parts: \( -15 + 80 = 65 \)
2. Imaginary parts: \( 40i + 30i = 70i \)
Putting it all together, the result is:
\[
65 + 70i
\]
Thus, the product \( (5 - 10i)(-3 + 8i) \) is:
\[
\boxed{65 + 70i}
\]
There are no human answers yet. A form for humans to post answers is coming very soon!