Multiply

Question

(
5
−
10
i
)
(
−
3
+
8
i
)


(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):

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

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:

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