How do I find the product of two imaginary numbers?

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Answer 1 · 2014-09-04T21:57:23

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

Ex: multiply #3i*-4i =#

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

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

... and then always substitute -1 for #i^2#:

#-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? #3i(4i - 6) =#

#=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