Simplify the following expression:

(3+7i)−(−6−3i)−(−7+4i)



Let's simplify the expression step by step:

Given:
\[
(3 + 7i) - (-6 - 3i) - (-7 + 4i)
\]

### Step 1: Remove parentheses by distributing the minus signs.

\[
(3 + 7i) - (-6 - 3i) = 3 + 7i + 6 + 3i
\]
\[
(3 + 7i + 6 + 3i) - (-7 + 4i) = 3 + 7i + 6 + 3i + 7 - 4i
\]

### Step 2: Combine the real and imaginary parts.

- Real parts: \(3 + 6 + 7 = 16\)
- Imaginary parts: \(7i + 3i - 4i = 6i\)

### Final Simplified Expression:
\[
16 + 6i
\]

Would you like more details on any of the steps?

Here are five questions to explore further:
1. How would you subtract complex numbers in polar form?
2. What is the geometric interpretation of complex number addition and subtraction?
3. Can you simplify \( (5 + 4i) - (2 - 7i) \)?
4. How do you multiply two complex numbers?
5. What is the magnitude of \(16 + 6i\)?

**Tip:** When simplifying complex expressions, always combine real and imaginary parts separately.

Simplify the following expression: (3+7i)−(−6−3i)−(−7+4i)

Learn how to simplify the complex expression (3 + 7i) − (−6 − 3i) − (−7 + 4i) by distributing minus signs and combining real and imaginary parts. This solution covers key concepts of complex numbers, including addition and subtraction. Suitable for students in Grades 9-11.

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