Question

What is the product of the multiplication (5−3i)(−2+6i)
?(1 point)
Responses

−28+36i
negative 28 plus 36 i

8+36i
8 plus 36 i

−10+18i
negative 10 plus 18 i

−10−18i

Answer 1

To find the product of the multiplication \((5 - 3i)(-2 + 6i)\), we can use the distributive property (also known as the FOIL method for binomials).

Here’s how the multiplication works:

\[
(5 - 3i)(-2 + 6i) = 5 \cdot (-2) + 5 \cdot 6i - 3i \cdot (-2) - 3i \cdot 6i
\]

Calculating each term:

1. \(5 \cdot (-2) = -10\)
2. \(5 \cdot 6i = 30i\)
3. \(-3i \cdot (-2) = 6i\)
4. \(-3i \cdot 6i = -18i^2\) (Recall that \(i^2 = -1\), so this becomes \(+18\))

Now, combine all the calculated terms together:

\[
-10 + 30i + 6i + 18
\]

Combine the real parts and the imaginary parts:

Real part: \(-10 + 18 = 8\)

Imaginary part: \(30i + 6i = 36i\)

Putting it all together, we have:

\[
8 + 36i
\]

So, the final answer is:

\[
\boxed{8 + 36i}
\]