# Complex numbers: Represent complex numbers in a form appropriate to the context

### Subject outcome

Subject outcome 1.1: Represent complex numbers in a form appropriate to the context

### Learning outcomes

- Write imaginary numbers in their simplest form where [latex]\scriptsize {{i}^{2}}=-1[/latex].
- Simplify negative roots into imaginary numbers.
- Simplify and perform addition, subtraction, multiplication and division on imaginary numbers.
- Construct Argand diagrams to find and represent the modulus and positive argument.
- Represent complex numbers in polar form with positive argument.

### Unit 1 outcomes

By the end of this unit you will be able to:

- Define imaginary numbers.
- Perform basic operations on imaginary numbers.
- Define complex numbers.
- Represent complex numbers in standard rectangular coordinate form.

### Unit 2 outcomes

By the end of this unit you will be able to:

- Represent complex numbers using an Argand diagram.
- Find the modulus and argument of a complex number [latex]\scriptsize {{i}^{2}}=-1[/latex].

### Unit 3 outcomes

By the end of this unit you will be able to:

- Express complex numbers in polar form.
- Convert complex numbers from standard/rectangular form to polar form.
- Convert complex numbers from polar form to standard/rectangular form.