Complex numbers quiz

Complex or imaginary numbers are a very abstract and diverse area of advanced mathematics. They are used by mathematicians, engineers, astrophysicists and cosmologists.

I have composed this quiz to test you on the fundamentals of complex numbers. The basic definitions that you need to know are the formulae in literal forms for addition, subtraction, multiplication and division of complex numbers. Also conjugate, modulus and argument.

Created by: mathemania

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  1. Which one of the following letters denotes the square root of -1 ?
  2. What are the solutions of the equation (z^2)+ 9 = 0 ?
  3. Given that w = 1 + 2i and z = 3 + i then w + z =
  4. Given that w = 5 + 2i and z = 2 + i then w - z =
  5. Given that w = 1 + 2i and z = 3 - i then wz =
  6. Given that w = i and z = 2 + i then w/z =
  7. Given that z = 2 + 3i z* =
  8. The modulus of the complex number 3 + 4i is
  9. The modulus of the complex number 1 + i is
  10. The reciprocal of the complex number 2 + 3i is
  11. Given that z = 1 + i arg z =
  12. Given that w = 4 + i and z = 1 - 2i w + z =
  13. Given that w = 2 + i and z = 1 + 3i w - z =
  14. Given that w = 1 + 2i and z = 2 + i wz =
  15. Given that w = 1 - i and z = 1 + i w/z =
  16. Given that z = 2 + 3i, z + z* =
  17. The modulus of the complex number 8 + 6i is
  18. (2 - 3i) / (1 + 4i) =
  19. Given that z = 1 + 4i, z^2 =
  20. What are the two square roots of 8i ?

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