SOLUTION: could someone please help me with this problem? (3-i) / (1+i) I know you use the conjugate and multiply by (3-i) / (1+I) I think,but I don't think I did something right.Thanks

Question 131945: could someone please help me with this problem?
(3-i) / (1+i) I know you use the conjugate and multiply by (3-i) / (1+I) I think,but I don't think I did something right.Thanks for your help in advance.
Sincerely,LH
Answer by solver91311(24713) (Show Source): 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.