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Let's simplify the expression \((4 + 9i) - (2 + 7i)\).

1. **Distribute the negative sign** to the terms inside the parentheses:
   \[
   (4 + 9i) - 2 - 7i
   \]

2. **Combine like terms**:
   - Real part: \(4 - 2 = 2\)
   - Imaginary part: \(9i - 7i = 2i\)

Thus, the simplified expression is:

\[
2 + 2i
\]

The correct answer is option **(c) 2 + 2i**.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How do you add and subtract complex numbers?
2. What is the difference between real and imaginary parts in complex numbers?
3. How can you multiply two complex numbers?
4. What is the conjugate of a complex number, and how is it used?
5. How do you find the modulus of a complex number?

**Tip:** When simplifying complex numbers, always group and operate separately on the real and imaginary parts.

Learn how to simplify the complex number expression (4 + 9i) - (2 + 7i) by distributing the negative sign and combining like terms. The final simplified result is 2 + 2i. This problem covers key concepts of complex number operations and is suitable for students in Grades 10-12.

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