SOLUTION: 5/(3+i) In this case the (i) stands for imaginary number. The answer is (3-i)/2. I don't know how my teacher came up with the answer. Thank you so much! Please respond as so

Question 34574This question is from textbook Algebra 2
: 5/(3+i)
In this case the (i) stands for imaginary number.
The answer is (3-i)/2.
I don't know how my teacher came up with the answer.
Thank you so much! Please respond as soon as possible! This question is from textbook Algebra 2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
5/(3+i)
Multiply numerator and denominator by (3-i) as follows:
[5(3-i)]/[(3+i)(3-i)]
Notice the denominator is in the form (a+b)(a-b)
so the denominator takes on the form a^2-b^2, as follows:
=[5(3-i)]/[3^2 - i^2]
But i^2=-1, as you probably just learned, so you get:
=[5(3-i)]/[9+1]
=[5(3-i)]/10
=(3-i)/2
Cheers,
Stan H.

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