https://file.aiquickdraw.com/mathbot/file/17301461900337s03ni82.jpg

Let's work through each question from the image.

### Question 1:
**Problem:** Simplify and put your answer in standard form with NO SPACES.
\[
-i + (19 + 22i) - (8 - 14i)
\]

**Solution:**
1. Distribute the negative sign for the last term:
   \[
   -i + (19 + 22i) - 8 + 14i
   \]
2. Now, combine the real parts and imaginary parts separately:
   - Real parts: \(19 - 8 = 11\)
   - Imaginary parts: \(-i + 22i + 14i = 35i\)
3. Combine these results to get:
   \[
   11 + 35i
   \]

**Answer:** \(11+35i\)

---

### Question 2:
**Problem:** Simplify \(-9i^{65}\)

**Solution:**
1. Recall that the powers of \(i\) repeat in a cycle every four terms:
   \[
   i^1 = i, \quad i^2 = -1, \quad i^3 = -i, \quad i^4 = 1
   \]
2. To find \(i^{65}\), we divide 65 by 4 and look at the remainder:
   \[
   65 \div 4 = 16 \text{ remainder } 1
   \]
   So, \(i^{65} = i^1 = i\).
3. Now, substitute back:
   \[
   -9i^{65} = -9i
   \]

**Answer:** \(-9i\)

---

Do you want more details on these solutions or have any questions? 

Here are some related questions for further practice:
1. How do you simplify expressions with complex numbers?
2. What is the pattern of powers of \(i\) and why do they repeat every four terms?
3. How do you add and subtract complex numbers?
4. What does it mean for a complex number to be in standard form?
5. How do you multiply complex numbers and simplify the result?

**Tip:** Remember that the powers of \(i\) cycle every four terms, so you can reduce high powers by finding the remainder when divided by 4.

Learn how to simplify complex numbers by combining like terms and using powers of i. This includes simplifying expressions like -i + (19 + 22i) - (8 - 14i) and -9i^65. Suitable for high school students in Grades 10-12.

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