New Zealand
Level 8 - NCEA Level 3

# Complex Numbers and 4 Operations

Lesson

In summary, here is how you undertake the four operations with complex numbers.  If you would like to go back to where we covered them in more depth click on the links below.

• To add an subtract complex numbers, add/subtract corresponding real and imaginary components.
• Follow all the other rules of algebraic convention

Multiplication

To multiply complex numbers, we follow the rules of algebraic conventions as well as remembering that $i\times i=-1$i×i=1

Division

Division of complex numbers is carried out by multiplying by a fraction constructed using the conjugate of the denominator. This removes the complex component from the denominator.

#### Worked Examples

##### QUESTION 1

Evaluate $\left(3+6i\right)+\left(7+3i\right)$(3+6i)+(7+3i).

##### QUESTION 2

Simplify $-6\left(3-5i\right)$6(35i).

##### QUESTION 3

Simplify $-2i\left(4-3i\right)^2$2i(43i)2, leaving your answer in terms of $i$i.

##### QUESTION 4

Find the value of $\frac{4+6i}{1+i}$4+6i1+i.

### Outcomes

#### M8-9

Manipulate complex numbers and present them graphically

#### 91577

Apply the algebra of complex numbers in solving problems