https://file.aiquickdraw.com/mathbot/file/1728448370324dkf1xb07.jpg

The problem shown is:

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

To multiply these complex numbers, we'll use the distributive property (FOIL method).

### Step-by-step solution:

1. Multiply the real and imaginary parts:
   \[
   (2)(5) + (2)(-3i) + (5i)(5) + (5i)(-3i)
   \]

2. Perform each multiplication:
   - \(2 \cdot 5 = 10\)
   - \(2 \cdot (-3i) = -6i\)
   - \(5i \cdot 5 = 25i\)
   - \(5i \cdot (-3i) = -15i^2\)

3. Simplify using \(i^2 = -1\):
   - \( -15i^2 = -15(-1) = 15 \)

4. Combine all the terms:
   \[
   10 + (-6i) + 25i + 15
   \]
   Simplifies to:
   \[
   (10 + 15) + (-6i + 25i) = 25 + 19i
   \]

### Final Answer:
\[
25 + 19i
\]

Would you like further clarification or details?

### Related questions:
1. What is the general form of a complex number?
2. How do you divide complex numbers?
3. How can you represent complex numbers geometrically?
4. What is the conjugate of a complex number and how is it used?
5. How do you find the magnitude of a complex number?

### Tip:
When multiplying complex numbers, remember to simplify \(i^2\) as \(-1\) to get a real number.

Multiply and simplify the following complex numbers: (2 + 5i) • (5 - 3i)

Learn how to multiply and simplify complex numbers using the distributive property. This detailed explanation covers the multiplication of (2 + 5i) and (5 - 3i), simplifying complex numbers, and using i^2 = -1. Ideal for high school students in Grades 10-12.

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