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Let's solve the given problem. We are asked to multiply two complex numbers: 

\[
(4 - i) \times (3 + i)
\]

To solve this, we will apply the distributive property (also known as FOIL when dealing with binomials):

\[
(4 - i)(3 + i) = 4(3 + i) - i(3 + i)
\]

Now, distribute each term:

1. \( 4(3 + i) = 4 \times 3 + 4 \times i = 12 + 4i \)
2. \( -i(3 + i) = -i \times 3 - i \times i = -3i - i^2 \)

Since \( i^2 = -1 \), we simplify the second part:

\[
-3i - i^2 = -3i - (-1) = -3i + 1
\]

Now, combine the real and imaginary parts:

\[
(12 + 4i) + (-3i + 1) = (12 + 1) + (4i - 3i) = 13 + i
\]

Thus, the product of the complex numbers in standard form is:

\[
13 + i
\]

Would you like more details or have any further questions? Here are some related questions:

1. What are the basic operations on complex numbers?
2. How do you convert complex numbers to polar form?
3. What is the geometric interpretation of multiplying complex numbers?
4. How can you use the distributive property to expand more complex expressions?
5. How does \( i^2 = -1 \) affect complex number calculations?

**Tip:** When multiplying complex numbers, always remember to simplify \( i^2 \) as \( -1 \) and combine like terms (real with real, imaginary with imaginary).

Learn how to multiply the complex numbers (4 - i)(3 + i) using the distributive property and simplify the result. This detailed explanation breaks down key steps and includes concepts of complex number multiplication and simplification. Suitable for high school students.

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