Let me verify each calculation in this worksheet to check if the answers are correct.
The absolute value of a complex number |a + bi| = √(a² + b²)
Left column:
1. |8 + 9i| = √(8² + 9²) = √(64 + 81) = √145 ✓
2. |4 + 9i| = √(4² + 9²) = √(16 + 81) = √97 ✓
3. |7| = 7 ✓ (this is just a real number, so its absolute value is itself)
4. |5 + 2i| = √(5² + 2²) = √(25 + 4) = √29 ✓
5. |1 + 3i| = √(1² + 3²) = √(1 + 9) = 10 ✓
Right column:
6. |9 + 7i| = √(9² + 7²) = √(81 + 49) = √130 ✓
7. |3 + i| = √(3² + 1²) = √(9 + 1) = √10 ✓
8. |8 + 3i| = √(8² + 3²) = √(64 + 9) = √73 ✓
9. |3 + 7i| = √(3² + 7²) = √(9 + 49) = 58 ✓
10. |4 + 4i| = √(4² + 4²) = √(16 + 16) = √32 = √(16 × 2) = 4√2 ✓
All calculations have been verified and are correct!
Final Answer:
All answers on the worksheet are correct:
- |8 + 9i| = √145
- |9 + 7i| = √130
- |4 + 9i| = √97
- |3 + i| = √10
- |7| = 7
- |8 + 3i| = √73
- |5 + 2i| = √29
- |3 + 7i| = 58
- |1 + 3i| = √10
- |4 + 4i| = 4√2
Parent Tip: Review the logic above to help your child master the concept of simplifying imaginary numbers worksheet.
