# Multiplying and dividing complex numbers

### Multiplying and dividing complex numbers

We will continue to explore other types of operations on complex numbers. This section will focus on performing multiplication and division on complex numbers.

#### Lessons

• 1.
Multiplying complex numbers
a)
$(3+i)\times(1+3i)$

b)
$(1-\sqrt{2}i)\times(-2+3\sqrt{2}i)$

c)
$(6-5i)\times(6+5i)$

• 2.
Dividing complex numbers
a)
$(1+2i)\div(3-i)$

b)
$\frac{5-\sqrt{5}i}{-4+\sqrt{5}i}$

c)
$\frac{2-3i}{3i+2}$

• 3.
Given that $z=5+6i$, determine $\overline{z}\cdot z$

• 4.
Given that $w=2-5i$, $z=3+6i$ determine $w \cdot \overline{z}$