4.02a-d Complex numbers: language and arithmetic Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What is the value of i^2 in complex number arithmetic?

   • -1
   • i
   • -i
   • 1

2. What is the imaginary part of the complex number 3 - 4i?

   • 4
   • -4
   • 3
   • -4i

3. What is the complex conjugate of the number 5 + 2i?

   • 2 + 5i
   • -5 - 2i
   • 5 - 2i
   • -5 + 2i

4. Which set of numbers contains both real and imaginary numbers?

   • Rational numbers
   • Irrational numbers
   • Integers
   • Complex numbers

5. What type of number is the product of any complex number and its conjugate?

   • Zero
   • Real number
   • Imaginary number
   • Complex unit

6. If z = a + bi, what expression is equal to Re(z)?

   • a + b
   • bi
   • b
   • a

7. What is the simplified value of i raised to the power 3?

   • 1
   • -1
   • i
   • -i

8. What is the simplified value of i raised to the power 4?

   • 1
   • i
   • -i
   • -1

9. What is the simplified result of adding 3 + 2i and 4 - 5i?

   • 7 + 3i
   • 1 - 3i
   • 7 - 7i
   • 7 - 3i

10. What is the result of subtracting 2 - 3i from 5 + i?

    • 3 - 2i
    • 3 + 4i
    • 7 - 2i
    • 3 + 2i

11. What is the product of the complex numbers 2 + i and 3 + 2i?

    • 6 + 2i
    • 4 + 3i
    • 4 + 7i
    • 8 + 7i

12. What is the value of the product (1 + 3i)(1 - 3i)?

    • -10
    • 8
    • 10
    • -8

13. What are the solutions to the quadratic equation x^2 + 16 = 0?

    • x = ±4
    • x = ±4i
    • x = -4
    • x = ±16i

14. What is the result of expressing 5 divided by 1 + 2i in standard form?

    • 1 + 2i
    • 1 - 2i
    • 5 - 10i
    • -1 + 2i

15. If a + bi = 4 - 7i, what is the exact value of b?

    • -7i
    • -7
    • 4
    • 7

16. What is the simplified value of i raised to the power 10?

    • -i
    • 1
    • -1
    • i

17. What are the roots of the quadratic equation x^2 - 4x + 13 = 0?

    • 2 ± 3i
    • 2 ± 6i
    • -2 ± 3i
    • 4 ± 3i

18. If 2z + z* = 9 + 2i, what is the complex number z?

    • 3 - 2i
    • 3 + 6i
    • 9 + 2i
    • 3 + 2i

19. If 3 + 4i is a root of x^2 + px + q = 0 with real coefficients, find q.

    • -25
    • 7
    • 25
    • 5

20. What is the result of dividing 2 + 3i by 1 - i?

    • 0.5 + 2.5i
    • -1 + 5i
    • -0.5 + 2.5i
    • 2.5 - 0.5i

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