2.1-2.2 Quadratic equations and complex arithmetic Quiz: Pearson Edexcel Further Maths, Unit 2

The 20 questions

1. What does the modulus of a complex number z = x + iy represent on an Argand diagram?

   • Its distance from the origin, equal to sqrt(x^2 + y^2)
   • Its angle measured from the positive real axis
   • The difference x - y between its real and imaginary parts
   • The product x y of its real and imaginary parts

2. Which number is the imaginary part of z = 3 - 4i?

   • 3
   • 4i
   • -4i
   • -4

3. What is the value of i^2?

   • 1
   • -1
   • i
   • -i

4. What is the real part of (2 + 3i)(1 - i)?

   • 5
   • 2
   • 1
   • -1

5. For a quadratic ax^2 + bx + c = 0 with real coefficients, what is the discriminant?

   • 4ac - b
   • b - 4ac
   • b^2 - 4ac
   • b^2 + 4ac

6. If the discriminant of a quadratic with real coefficients is negative, what type of roots does it have?

   • Two distinct real roots
   • A pair of complex conjugate roots
   • Two equal real roots
   • One real root and one zero root

7. Which quadratic equation with real coefficients has roots 2 + i and 2 - i?

   • x^2 - 2x + 5 = 0
   • x^2 - 4x - 5 = 0
   • x^2 - 4x + 5 = 0
   • x^2 + 4x + 5 = 0

8. Solve x^2 + 4x + 13 = 0 over the complex numbers.

   • x = -2 + sqrt(13)i or x = -2 - sqrt(13)i
   • x = 2 + 3i or x = 2 - 3i
   • x = -4 + 3i or x = -4 - 3i
   • x = -2 + 3i or x = -2 - 3i

9. Solve x^2 - 6x + 10 = 0 over the complex numbers.

   • x = 6 + i or x = 6 - i
   • x = 3 + sqrt(10)i or x = 3 - sqrt(10)i
   • x = -3 + i or x = -3 - i
   • x = 3 + i or x = 3 - i

10. Express (3 + 2i)/(1 - i) in the form x + iy.

    • (5 + i)/2
    • (5 - i)/2
    • (1 - 5i)/2
    • (1 + 5i)/2

11. What is the product (1 + 2i)(3 - i)?

    • 5 - 5i
    • 5 + i
    • 1 + 5i
    • 5 + 5i

12. What is (2 - i)^2 in the form x + iy?

    • 4 + 4i
    • 5 - 4i
    • 3 + 4i
    • 3 - 4i

13. A real quadratic x^2 + px + q = 0 has root 1 + i. What are p and q?

    • p = 2 and q = 2
    • p = 2 and q = -2
    • p = -2 and q = -2
    • p = -2 and q = 2

14. Which of these is a square root of 3 + 4i?

    • 1 - 2i
    • 2 + i
    • 1 + 2i
    • 2 - i

15. For (1 + ai)(2 - i) to be real, what is the value of the real number a?

    • a = 2
    • a = -2
    • a = 1/2
    • a = -1/2

16. Which complex number is a root of z^3 - 2z^2 + 4z - 8 = 0?

    • -2
    • 1 + i
    • 2i
    • 1 - 2i

17. A real quadratic x^2 + kx + 10 = 0 has the root 1 + 3i. What is the value of k?

    • k = -2
    • k = -10
    • k = -1
    • k = 2

18. Find all complex numbers z = x + iy with real x and y satisfying z^2 = 5 + 12i.

    • 3 + 2i and -3 - 2i
    • 3 - 2i and -3 + 2i
    • 5 + 12i and -5 - 12i
    • 2 + 3i and -2 - 3i

19. Which real quadratic equation has roots 4 + 3i and 4 - 3i?

    • x^2 - 7x + 25 = 0
    • x^2 - 8x + 25 = 0
    • x^2 + 8x + 25 = 0
    • x^2 - 8x - 25 = 0

20. A quadratic x^2 + bx + c = 0 with real b and c has the root 2 - 3i. Which pair of values must hold?

    • b = 2 and c = -3
    • b = 4 and c = 13
    • b = -4 and c = 13
    • b = -4 and c = 5

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