Adding Subtracting Multiplying Complex Numbers Independent ... - Free Printable

Sure! Let’s solve each of the 10 problems step by step. These involve adding, subtracting, and multiplying complex numbers.

Recall:
- A complex number is written as \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.
- When adding/subtracting: combine like terms (real with real, imaginary with imaginary).
- When multiplying: use distributive property (FOIL if needed) and remember \( i^2 = -1 \).

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Problem 1: \( (4 + 8i) + (3 + 15i) \)

Add real parts: \( 4 + 3 = 7 \)
Add imaginary parts: \( 8i + 15i = 23i \)
✔ Answer: \( 7 + 23i \)

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Problem 2: \( 5(2 + 4i) \)

Distribute the 5:
\( 5 \cdot 2 = 10 \)
\( 5 \cdot 4i = 20i \)
✔ Answer: \( 10 + 20i \)

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Problem 3: \( (3 - 13i) - (14 + 5i) \)

Subtract real parts: \( 3 - 14 = -11 \)
Subtract imaginary parts: \( -13i - 5i = -18i \)
✔ Answer: \( -11 - 18i \)

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Problem 4: \( 6(5 + 8i) \)

Distribute the 6:
\( 6 \cdot 5 = 30 \)
\( 6 \cdot 8i = 48i \)
✔ Answer: \( 30 + 48i \)

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Problem 5: \( (15 - 13i) - (18 + 3i) \)

Real: \( 15 - 18 = -3 \)
Imaginary: \( -13i - 3i = -16i \)
✔ Answer: \( -3 - 16i \)

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Problem 6: \( (7 + 22i) + (15 - 4i) \)

Real: \( 7 + 15 = 22 \)
Imaginary: \( 22i - 4i = 18i \)
✔ Answer: \( 22 + 18i \)

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Problem 7: \( (2 + 18i) + (5 + 5i) \)

Real: \( 2 + 5 = 7 \)
Imaginary: \( 18i + 5i = 23i \)
✔ Answer: \( 7 + 23i \)

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Problem 8: \( 5(7 + 9i) \)

Distribute the 5:
\( 5 \cdot 7 = 35 \)
\( 5 \cdot 9i = 45i \)
✔ Answer: \( 35 + 45i \)

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Problem 9: \( (7 + 5i) + (8 - 4i) \)

Real: \( 7 + 8 = 15 \)
Imaginary: \( 5i - 4i = 1i = i \)
✔ Answer: \( 15 + i \)

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Problem 10: \( (8 - 17i) - (13 - 5i) \)

Real: \( 8 - 13 = -5 \)
Imaginary: \( -17i - (-5i) = -17i + 5i = -12i \)
✔ Answer: \( -5 - 12i \)

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## ✔ Final Answers:

1. \( 7 + 23i \)
2. \( 10 + 20i \)
3. \( -11 - 18i \)
4. \( 30 + 48i \)
5. \( -3 - 16i \)
6. \( 22 + 18i \)
7. \( 7 + 23i \)
8. \( 35 + 45i \)
9. \( 15 + i \)
10. \( -5 - 12i \)

Let me know if you’d like to see any step shown in more detail!