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