## Adding Complex Numbers: (−4+10i)+(5+3i)

This article will guide you through the process of adding two complex numbers: (−4+10i) and (5+3i).

### Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form **a + bi**, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as the square root of -1.

### Adding Complex Numbers

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

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

- For (−4+10i):
- Real part: -4
- Imaginary part: 10

- For (5+3i):
- Real part: 5
- Imaginary part: 3

**Step 2:** Add the real parts: -4 + 5 = 1

**Step 3:** Add the imaginary parts: 10 + 3 = 13

**Step 4:** Combine the results to get the final complex number: **1 + 13i**

### Conclusion

Therefore, the sum of (−4+10i) and (5+3i) is **1 + 13i**. This process demonstrates the simplicity of adding complex numbers. It's important to remember that complex numbers are added by combining their real and imaginary components separately.