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Let's solve the expression \((5 + i)(5 - i)\).

This is a product of two complex numbers in the form of a difference of squares:

\[
(5 + i)(5 - i) = 5^2 - i^2
\]

We know that \(i^2 = -1\), so:

\[
(5 + i)(5 - i) = 5^2 - (-1) = 25 + 1 = 26
\]

The correct answer is **26**.

Would you like more details on any part of this solution? Here are 5 related questions to expand your understanding:

1. How do we multiply two complex numbers in general?
2. What is the geometric interpretation of multiplying complex conjugates?
3. Can you explain the difference between real and imaginary parts in a complex number?
4. How does the identity \(i^2 = -1\) help simplify complex number multiplication?
5. Why does multiplying conjugates of a complex number result in a real number?

**Tip:** When multiplying complex conjugates, the result is always a real number because the imaginary parts cancel each other out.

Solve the complex number multiplication problem (5 + i)(5 - i). Learn how to apply the difference of squares formula to simplify this expression and understand how i^2 = -1 works in complex numbers. Suitable for students in Grades 10-12.

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