We use the multiplication property of complex number and its conjugate to divide two complex numbers.

__Example:__ Express in the form of a complex number a + b i.

We first multiply the numerator and denominator by the complex conjugate of the denominator

[ (8 + 4 i)(1 + i) ]

Multiply and group like terms

[ (8 + 4 i)(1 + i) ] / [ (1 - i)(1 + i) ] =

[ 8 + 4 i + 8 i + 4 i^{ 2} ] / [ 1 - i + i - i^{ 2} ]

= (4 + 12 i ) / (2)

= 2 + 6 i

**Applet that divides two complex numbers: enter your complex numbers and press enter**

__Exercises__

- Find the complex conjugate of the following complex numbers

a) 2 + 6 i

b) -8 i

c) 12

- Write the following expressions in the form a + b i

a) (2 - 8 i) + (-6 i)

b) -8 i + (3 - 9 i)

c) 6 - (3 - i)

d) (2 - 3 i)(7 - i)

e) (2 + 2 i) / (2 - 2i)

__Solutions to above exercises__

- Find the complex conjugate.

a) 2 - 6 i

b) 8 i

c) 12

- Write the following expressions in the form a + b i

a) (2 - 8 i) + (-6 i) = 2 - 14 i

b) -8 i + (3 - 9 i) = 3 - 17 i

c) 6 - (3 - i) = 3 + i

d) (2 - 3 i)(7 - i) = 11 - 23 i

e) (2 + 2 i) / (2 - 2i) = i