Exam Questions - Complex numbers

Exam Questions - Complex numbers

Complex Numbers - Question Types

Arithmetic with Complex Numbers

  • Questions may require the addition, subtraction, multiplication or division of complex numbers.
  • In these cases, use the definition of complex numbers p + qi and apply basic arithmetic rules.
  • Be aware of how to multiply complex numbers by their conjugates and how this simplifies the equation.

Complex Conjugates and Modulus

  • The exam may feature questions about the complex conjugate of a given complex number.
  • Remember that the complex conjugate of a + bi is a - bi.
  • Questions may also involve finding the modulus of a complex number, remember this is the distance from the origin to the point represented by the complex number on the Argand diagram.

Argand Diagrams

  • Some questions may require drawing or interpreting Argand diagrams.
  • Be aware of what the various parts of the diagram represent, such as the real axis, the imaginary axis, and how to identify complex numbers on the diagram.

Polynomials with Complex Roots

  • Polynomials that have complex roots may be a part of the question.
  • Given a polynomial, you may be asked to find complex roots or asked to interpret their significance.
  • Remember to apply the principle of the conjugate root theorem if you find one root to be a complex number.

Exponentials and Logarithms of Complex Numbers

  • Questions may involve the use of exponents or logarithms with complex numbers.
  • Be prepared to apply the rules of indices and logarithmic identities with complex numbers.

Using De Moivre’s Theorem

  • De Moivre’s theorem may be used to solve problems involving roots of complex numbers or finding the powers of complex numbers.
  • Questions about De Moivre’s theorem require knowledge of trigonometric identities and the understanding of complex numbers in polar form.

Tips for Solving Complex Number Questions

Preparing for Questions

  • Practice a wide range of problems from each of these types of complex number questions to become familiar with the techniques required.

During the Exam

  • Ensure you show each step of your working out, even for seemingly simple calculations. Marks are often awarded for ‘method’.
  • Be methodical and don’t rush. Complex number questions often have multiple parts but being systematic can help ensure you don’t miss anything.
  • Finally, make sure to check your answers. A quick look over your calculations can catch any simple mistakes that might cost you valuable marks.