Question

Distribute to simplify the expression (3i + 4)(−2i − 5)
.(1 point)
+
i

Answer 1

To simplify the expression \((3i + 4)(-2i - 5) + i\), we will first distribute the terms in the parentheses.

1. Distribute \((3i + 4)\) and \((-2i - 5)\):

\[
(3i + 4)(-2i) + (3i + 4)(-5)
\]

- For \((3i + 4)(-2i)\):

\[
3i \cdot (-2i) + 4 \cdot (-2i) = -6i^2 - 8i
\]

- For \((3i + 4)(-5)\):

\[
3i \cdot (-5) + 4 \cdot (-5) = -15i - 20
\]

2. Now add these results together:

\[
-6i^2 - 8i - 15i - 20 = -6i^2 - 23i - 20
\]

3. Recall that \(i^2 = -1\):

\[
-6(-1) - 23i - 20 = 6 - 23i - 20
\]

4. Simplifying the constants:

\[
6 - 20 = -14
\]

Putting it all together, we have:

\[
-14 - 23i
\]

5. Finally, add \(i\):

\[
-14 - 23i + i = -14 - 22i
\]

Thus, the simplified expression is:

\[
\boxed{-14 - 22i}
\]