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A conjugate of a complex number
is formed by changing the sign on the imaginary part. So the conjugate of
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
The conjugate of the denominator is
, so you need to multiply the entire expression by
Now multiply numerator times numerator and denominator times denominator just like multiplying any other pair of fractions.
Using FOIL, the numerator product becomes:
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