Question

Multiply the complex numbers. Type the answer into the box.

(4-7i)(2+5i) =

Answer 1

To multiply the complex numbers \( (4 - 7i)(2 + 5i) \), we can use the distributive property (also known as the FOIL method for binomials).

Let's compute it step by step:

1. Multiply the real parts:
\[
4 \times 2 = 8
\]

2. Multiply the outer parts:
\[
4 \times 5i = 20i
\]

3. Multiply the inner parts:
\[
-7i \times 2 = -14i
\]

4. Multiply the imaginary parts:
\[
-7i \times 5i = -35i^2
\]
Since \( i^2 = -1 \), this becomes:
\[
-35(-1) = 35
\]

Now, we add all these results together:
\[
8 + 20i - 14i + 35
\]

Combine like terms (real and imaginary):
1. Real parts: \( 8 + 35 = 43 \)
2. Imaginary parts: \( 20i - 14i = 6i \)

Putting it all together, we have:
\[
43 + 6i
\]

Thus, the product of the complex numbers \( (4 - 7i)(2 + 5i) \) is:
\[
\boxed{43 + 6i}
\]