Problem: Solve the given operations involving complex numbers.
#### Recall:
A complex number is of the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. When performing arithmetic operations on complex numbers:
- Addition and subtraction are done by combining the real parts and the imaginary parts separately.
- The imaginary unit \( i \) satisfies \( i^2 = -1 \).
Let's solve each problem step by step.
---
Problem 1: \( (16 - 4i) - (12 - 3i) \)
1. Distribute the negative sign across the second complex number:
\[
(16 - 4i) - (12 - 3i) = 16 - 4i - 12 + 3i
\]
2. Combine the real parts:
\[
16 - 12 = 4
\]
3. Combine the imaginary parts:
\[
-4i + 3i = -i
\]
4. Write the final result:
\[
4 - i
\]
Answer for Problem 1:
\[
\boxed{4 - i}
\]
---
Problem 2: \( (3i + 7) + (34 - 6i) \)
1. Rearrange the terms to group the real parts and the imaginary parts:
\[
(3i + 7) + (34 - 6i) = 7 + 34 + 3i - 6i
\]
2. Combine the real parts:
\[
7 + 34 = 41
\]
3. Combine the imaginary parts:
\[
3i - 6i = -3i
\]
4. Write the final result:
\[
41 - 3i
\]
Answer for Problem 2:
\[
\boxed{41 - 3i}
\]
---
Problem 3: \( (-4 + 7i) + (8 - 9i) \)
1. Rearrange the terms to group the real parts and the imaginary parts:
\[
(-4 + 7i) + (8 - 9i) = -4 + 8 + 7i - 9i
\]
2. Combine the real parts:
\[
-4 + 8 = 4
\]
3. Combine the imaginary parts:
\[
7i - 9i = -2i
\]
4. Write the final result:
\[
4 - 2i
\]
Answer for Problem 3:
\[
\boxed{4 - 2i}
\]
---
Problem 4: \( (-1 - i) - (-3 - 4i) \)
1. Distribute the negative sign across the second complex number:
\[
(-1 - i) - (-3 - 4i) = -1 - i + 3 + 4i
\]
2. Combine the real parts:
\[
-1 + 3 = 2
\]
3. Combine the imaginary parts:
\[
-i + 4i = 3i
\]
4. Write the final result:
\[
2 + 3i
\]
Answer for Problem 4:
\[
\boxed{2 + 3i}
\]
---
Final Answers:
1. \(\boxed{4 - i}\)
2. \(\boxed{41 - 3i}\)
3. \(\boxed{4 - 2i}\)
4. \(\boxed{2 + 3i}\)
Parent Tip: Review the logic above to help your child master the concept of adding subtracting complex numbers worksheet.
