Question

Mutiply (5-10i)(-3+8i) provide answer simplified to the finest and for a+bi

Answer 1

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

1. **First**: Multiply the real parts:
\[
5 \cdot -3 = -15
\]

2. **Outer**: Multiply the outer parts:
\[
5 \cdot 8i = 40i
\]

3. **Inner**: Multiply the inner parts:
\[
-10i \cdot -3 = 30i
\]

4. **Last**: Multiply the imaginary parts:
\[
-10i \cdot 8i = -80i^2
\]
Since \( i^2 = -1 \), this becomes:
\[
-80(-1) = 80
\]

Now combine all these results:
\[
-15 + 40i + 30i + 80
\]

Combine like terms:
\[
(-15 + 80) + (40i + 30i) = 65 + 70i
\]

So, the product \( (5 - 10i)(-3 + 8i) \) simplifies to:
\[
\boxed{65 + 70i}
\]