# 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 $\scriptsize i$-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.