Complex Numbers: Working with complex numbers
Subject outcome
Subject outcome 1.1: Work with complex numbers
Learning outcomes
- Perform addition, subtraction, multiplication and division on complex numbers in standard form (includes [latex]\scriptsize i[/latex]-notation).
Note: Leave answers with positive argument. - Perform multiplication and division on complex numbers in polar form.
- Use De Moivre’s theorem to raise complex numbers to powers (excluding fractional powers).
- Convert the form of complex numbers where needed to enable performance of advanced operations on complex numbers (a combination of standard and polar form may be assessed in one expression).
Unit 1 outcomes
By the end of this unit you will be able to:
- Add complex numbers in standard form.
- Subtract complex numbers in standard form.
- Multiply complex numbers in standard form.
- Divide complex numbers in standard form through the use of a suitable conjugate.
Unit 2 outcomes
By the end of this unit you will be able to:
- Plot a complex number on the complex plan.
- Find the absolute value of a complex number.
- Convert a complex number from standard (or rectangular) form to polar form.
- Convert a complex number from polar form to standard (or rectangular) form.
- Understand what is meant by the abbreviation when dealing with complex numbers in polar
Unit 3 outcomes
By the end of this unit you will be able to:
- Multiply complex numbers in polar form.
- Divide complex numbers in polar form.
Unit 4 outcomes
By the end of this unit you will be able to:
- Find the powers of complex numbers in polar form.
- Simplify complex expressions with powers.
