Simplify the expression to a + bi form: (−12−7i)−(−11−2i)

To simplify the expression \((−12 − 7i) − (−11 − 2i)\) to the form \(a + bi\), we need to distribute the negative sign and then combine like terms.

### Step-by-Step Solution:

1. Distribute the negative sign to the second complex number:

   \[
   (−12 − 7i) − (−11 − 2i) = (−12 − 7i) + (11 + 2i)
   \]

2. **Add the real parts**: \(-12 + 11 = -1\).

3. **Add the imaginary parts**: \(-7i + 2i = -5i\).

So, the simplified expression is:

\[
(−12 − 7i) − (−11 − 2i) = -1 - 5i
\]

### Final Answer:
\[
-1 - 5i
\]

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you subtract complex numbers?
2. What is the magnitude of the complex number \(-1 - 5i\)?
3. How can you plot a complex number on the complex plane?
4. How do you find the argument of a complex number?
5. What happens when you multiply a complex number by its conjugate?

**Tip:** Remember to distribute the negative sign when subtracting complex numbers before combining like terms!

Learn how to simplify the expression (−12 − 7i) − (−11 − 2i) to the form a + bi using step-by-step instructions. This problem covers complex number subtraction and is suitable for high school level students.

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