# 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.