Question

How do you rationalize imaginary denominators?

Answer 1

If `a + bi` is an imaginary number
its conjugate is `a-bi` (also an imaginary number)
and
the product of an imaginary number and its conjugate it not an imaginary number.
`(a+bi)xx(a-bi) = a^2 - b^2`

If you have a number with an imaginary denominator multiply both the numerator and denominator by the conjugate of the denominator.

For example, suppose you want to rationalize the denominator of
`(10)/(3+2i)`

`(10)/(3+2i) *(3-2i)/(3-2i)`

`=(10(3-2i))/(3^2 - 2^2)`

`= (30-20i)/(9-4)`

`= 6-4i`