Question

Multiply (5−10i)(−3+8i)
(1 point)

Answer 1

To multiply the complex numbers \( (5 - 10i)(-3 + 8i) \), we can use the distributive property (also known as the FOIL method for binomials):

\[
(5 - 10i)(-3 + 8i) = 5 \cdot (-3) + 5 \cdot (8i) - 10i \cdot (-3) - 10i \cdot (8i)
\]

Calculating 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 can simplify \( -80i^2 \):

\[
-80i^2 = -80(-1) = 80
\]

Now we combine all the terms:

\[
-15 + 40i + 30i + 80 = (-15 + 80) + (40i + 30i) = 65 + 70i
\]

Thus, the result of multiplying \( (5 - 10i)(-3 + 8i) \) is:

\[
\boxed{65 + 70i}
\]