# How do I find the product of two imaginary numbers?

##### 1 Answer

First, complex numbers can come in a variety of forms!

Ex: multiply

Remember, with multiplication you can rearrange the order (called the Commutative Property):

#3*-4*i*i =-12i^2#

... and then always substitute -1 for

#-12*-1 = 12#

Ex: the numbers might come in a radical form:

#sqrt(-3)*4sqrt(-12) =#

You should always "factor" out the imaginary part from the square roots like this:

#sqrt(-1)sqrt(3)*4*sqrt(-1)sqrt(4)sqrt(3) =#

and simplify again:

#=i*4*sqrt(3)*sqrt(3)*sqrt(4)#

#=i*4*3*2 = 24i#

Ex: what about the Distributive Property?

#=12i^2- 18i#

#=12(-1) - 18i#

#= -12 - 18i#

And last but not least, a pair of binomials in a + bi form:

Ex: (3 - 2i)(4 + i) =

=12 + 3i - 8i -

#2i^2#

= 12 - 2(-1) + 3i - 8i

= 12 + 2 - 5i

= 14 - 5i