Question 219581
{{{6/(5+i)}}} Start with the given expression.



{{{(6/(5+i))((5-i)/(5-i))}}} Multiply the fraction by {{{(5-i)/(5-i)}}}.



{{{(6(5-i))/((5+i)(5-i))}}} Combine the fractions.



{{{((6)(5)+(6)(-i))/((5+i)(5-i))}}} Distribute



{{{((6)(5)+(6)(-i))/((5)(5)+(5)(-i)+(i)(5)+(i)(-i))}}} FOIL the denominator.



{{{(30-6i)/(25-5i+5i-i^2)}}} Multiply.



{{{(30-6i)/(25-5i+5i-(-1))}}} Replace {{{i^2}}} with -1.



{{{(30-6i)/(25-5i+5i+1)}}} Simplify



{{{(30-6i)/(26)}}} Combine like terms.



{{{(30)/(26)+((-6)/(26))i}}} Break up the fraction.



{{{15/13-(3/13)i}}} Reduce.



So {{{6/(5+i)=15/13-(3/13)i}}} which is in standard form {{{a+bi}}} where {{{a=15/13}}} and {{{b=-3/13}}}