You can
put this solution on YOUR website!A conjugate of a complex number
is formed by changing the sign on the imaginary part. So the conjugate of
is
.
To simplify an expression with a complex denominator, you need to multiply the entire expression by 1 in the form of the conjugate of the denominator divided by itself. That means if you have
, you want to multiply by 1 in the form of
.
Your problem:
The conjugate of the denominator is
, so you need to multiply the entire expression by
, thus:
Now multiply numerator times numerator and denominator times denominator just like multiplying any other pair of fractions.
Using FOIL, the numerator product becomes:
(remember
so
)
The denominator product is easier because, by using the conjugate, you have the factors of the difference of two squares, so
Putting the pieces back together we have
Done.
