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 $w \cdot \overline{z}$