SOLUTION: Simplify
1/2-i
Algebra.Com
Question 184324: Simplify
1/2-i
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You really need to use parentheses so that it is clear what you mean. Here, you might mean:
In which case, this is already simplified as much as possible.
On the other hand if you meant, as I suspect:
Then you really should have rendered your problem thus: 1/(2 - i).
Having said all that,
First determine the conjugate of the denominator. The conjugate of any binomial is the same binomial with the sign in the middle changed. Hence, the conjugate of 
, for example, is 
. In this problem the conjugate of your denominator is:
Multiply your original fraction by 1 in the form of the conjugate of the denominator divided by itself:
\left(\frac{2 + i}{2 + i}\right))
Using the difference of two squares factorization, this becomes:
}=\frac{2+i}{5})
John
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