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Quiz

Year 3: Complex numbers

10 questions with solutions for year 3: sums and differences, modulus and distance, trigonometric form, multiplying, dividing and powers, quadratic equations – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. z₁ = 2 + 5i, z₂ = 3 + 2i. z₁ + z₂ = ?

2. z₁ = 4 + 3i, z₂ = 1 − i. z₁ − z₂ = ?

3. The modulus of 12 − 5i?

4. The distance between the points 5 − i and −3 + 5i is:

5. Trigonometric form of √3 + i:

6. 5(cos 40° + i sin 40°) · 3(cos 50° + i sin 50°) = ?

7. (cos 130° + i sin 130°) : (cos 40° + i sin 40°) = ?

8. (i − 1)⁷ / (1 + i)⁵ = ?

9. The solutions of x² − 4x + 20 = 0 are:

10. A quadratic with real coefficients and roots 2 + i and 2 − i: