Question 189232
{{{(2-i)/(5+i)}}} Start with the given expression.



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



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



{{{((2)(5)+(2)(-i)+(-i)(5)+(-i)(-i))/((5+i)(5-i))}}} FOIL the numerator.



{{{((2)(5)+(2)(-i)+(-i)(5)+(-i)(-i))/((5)(5)+(5)(-i)+(i)(5)+(i)(-i))}}} FOIL the denominator.



{{{(10-2i-5i+i^2)/(25-5i+5i-i^2)}}} Multiply.



{{{(9-7i)/(26)}}} Combine like terms.



{{{(9)/(26)+((-7)/(26))i}}} Break up the fraction.



{{{9/26-(7/26)i}}} Reduce.



So {{{(2-i)/(5+i)=9/26-(7/26)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=9/26}}} and {{{b=-7/26}}}