Complex Numbers – Square Roots, Quadratic Equations with Complex Roots

Grade 11 Maths Higher — Complex Numbers – Square Roots, Quadratic Equations with Complex Roots: 25 practice questions with instant scoring and explanations.

1. The square roots of -1 are:
2. The square root of i is:
3. For the quadratic equation x² + 1 = 0, the roots are:
4. The discriminant of ax² + bx + c = 0 is Δ = b² - 4ac. When Δ < 0, the roots are:
5. For the equation x² - 2x + 2 = 0, the roots are:
6. The square roots of 3 + 4i are:
7. If z² = -8, then z =
8. For a quadratic equation with complex roots α and β, the sum α + β =
9. If the roots of x² + px + q = 0 are complex, what can be said about p² - 4q?
10. The square roots of -5 are:
11. For x² - 4x + 5 = 0, the roots are:
12. If one root of a quadratic with real coefficients is 2 + 3i, the other root is:
13. The square root of 5 - 12i is:
14. For the equation x² + x + 1 = 0, the roots in terms of ω are:
15. If α = 1 + i and β = 1 - i are roots of ax² + bx + c = 0, then b/a =
16. The modulus of the roots of x² + 2x + 5 = 0 is:
17. For x² - 6x + 13 = 0, the roots are:
18. If z is a complex number with |z| = 2 and z² = -4, then z =
19. The quadratic equation with roots i and -i is:
20. For the equation x² + 2x + 2 = 0, find |root₁ · root₂|:
21. The square roots of 7 + 24i are:
22. If α + β = 3 and αβ = 4 where α, β are roots of x² + px + q = 0, then p + q =
23. For x² + px + p = 0 to have complex roots, the range of p is:
24. The square root of -9 + 40i is:
25. If z = 2 - 2i, then z² =