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
