# 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 $\scriptsize {{i}^{2}}=-1$.
• 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 $\scriptsize {{i}^{2}}=-1$.

### 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.