Complex numbers

Adding, multiplying and taking powers of i — the whole of a first meeting with complex numbers.

3 sheets · 30 questions · one answer key · 4 pages

Recommended for grades 10–11

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Add and subtract Sheet 1 of 3

Complex numbersAdding and subtracting

Name: Date:

Add or subtract each pair of complex numbers.

1(−1 − 4i) − (−2 + 4i)

2(5 − 2i) − (4 + 2i)

3(−5 + 3i) − (−5 + 6i)

4(−2 − 3i) + (−2 − 3i)

5(2 − i) + (−3 − 2i)

6(6 − 4i) + (−2 + 4i)

7(−1 − 5i) + (6 − 6i)

8(1 + 6i) + (1 − 4i)

9(1 − 3i) − (−2 − 3i)

10(2 − 5i) − (−1 − 3i)

Complex numbersMultiplying

Name: Date:

Multiply each pair of complex numbers.

1(3 + 2i)(−4 − 2i)

2(3 − 5i)(−1 − 3i)

3(2 − 6i)(6 + i)

4(−2 + 3i)(−5 + 6i)

5(−4 − 6i)(−6 − 6i)

6(−4 + 6i)(−6 − i)

7(6 + 4i)(−5 − i)

8(−2 − 4i)(5 + i)

9(−1 + 2i)(3 − 5i)

10(1 + 3i)(2 + 3i)

Complex numbersPowers of i

Name: Date:

Work out each power of i.

1i⁶

2i²³

3i¹⁶

4i¹⁵

5i⁵

6i⁸

7i²

8i²⁰

9i¹¹

10i¹⁰

Power Pack · Complex numbersAnswer key

Add and subtract

1. (−1 − 4i) − (−2 + 4i) = 1 − 8i2. (5 − 2i) − (4 + 2i) = 1 − 4i3. (−5 + 3i) − (−5 + 6i) = −3i4. (−2 − 3i) + (−2 − 3i) = −4 − 6i5. (2 − i) + (−3 − 2i) = −1 − 3i6. (6 − 4i) + (−2 + 4i) = 47. (−1 − 5i) + (6 − 6i) = 5 − 11i8. (1 + 6i) + (1 − 4i) = 2 + 2i9. (1 − 3i) − (−2 − 3i) = 310. (2 − 5i) − (−1 − 3i) = 3 − 2i

Multiply

1. (3 + 2i)(−4 − 2i) = −8 − 14i2. (3 − 5i)(−1 − 3i) = −18 − 4i3. (2 − 6i)(6 + i) = 18 − 34i4. (−2 + 3i)(−5 + 6i) = −8 − 27i5. (−4 − 6i)(−6 − 6i) = −12 + 60i6. (−4 + 6i)(−6 − i) = 30 − 32i7. (6 + 4i)(−5 − i) = −26 − 26i8. (−2 − 4i)(5 + i) = −6 − 22i9. (−1 + 2i)(3 − 5i) = 7 + 11i10. (1 + 3i)(2 + 3i) = −7 + 9i

Powers of i

1. i⁶ = −12. i²³ = −i3. i¹⁶ = 14. i¹⁵ = −i5. i⁵ = i6. i⁸ = 17. i² = −18. i²⁰ = 19. i¹¹ = −i10. i¹⁰ = −1

Complex numbers

What is in the pack

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