## Adding Complex Numbers: (5 + 2i) + (3 - 2i)

This article will guide you through the process of adding two complex numbers: (5 + 2i) and (3 - 2i).

### Understanding Complex Numbers

Complex numbers are numbers that consist of two parts: a **real part** and an **imaginary part**. The imaginary part is denoted by the letter 'i', where **i² = -1**.

### Adding Complex Numbers

Adding complex numbers is straightforward. We simply add the real parts together and the imaginary parts together separately.

**Step 1: Identify the real and imaginary parts of each number:**

- (5 + 2i) has a real part of 5 and an imaginary part of 2i.
- (3 - 2i) has a real part of 3 and an imaginary part of -2i.

**Step 2: Add the real parts together:**

- 5 + 3 = 8

**Step 3: Add the imaginary parts together:**

- 2i + (-2i) = 0

**Step 4: Combine the results:**

- 8 + 0 =
**8**

Therefore, (5 + 2i) + (3 - 2i) = **8**.

**Important Note:** The imaginary part cancels out in this specific example. This is not always the case when adding complex numbers.

### Conclusion

Adding complex numbers is a simple process involving combining the real and imaginary parts separately. This allows us to manipulate and work with complex numbers effectively in various mathematical contexts.