https://file.aiquickdraw.com/mathbot/file/1729368293956ark8vxmd.jpg

The problem is to simplify the following complex number expression:

\[
(4 - 2i) + (6 - 3i) - (-5 - 5i).
\]

Let's simplify this step by step:

1. **Distribute the negative sign** over the last term:
   \[
   (4 - 2i) + (6 - 3i) + (5 + 5i).
   \]

2. **Combine the real parts**:
   \[
   4 + 6 + 5 = 15.
   \]

3. **Combine the imaginary parts**:
   \[
   -2i - 3i + 5i = 0i.
   \]

So the simplified expression is:

\[
15 + 0i = 15.
\]

The correct answer is \( \boxed{15} \).

Would you like more details on this solution or have any other questions?

### Related questions:
1. What are complex numbers and how are they defined?
2. How do you add and subtract complex numbers?
3. What are real and imaginary components of a complex number?
4. How can you graph complex numbers in the complex plane?
5. What are the practical applications of complex numbers?

### Tip:
Always combine the real and imaginary parts separately when simplifying complex numbers.

Simplify (4 - 2i) + (6 - 3i) - (-5 - 5i).

Learn how to simplify the complex number expression (4 - 2i) + (6 - 3i) - (-5 - 5i). This step-by-step solution covers key concepts in complex number operations, focusing on combining real and imaginary parts separately.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation