Question 306966
{{{(2-i)/(5+2i)}}} Start with the given expression.



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



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



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



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



{{{(10-4i-5i+2i^2)/(25-10i+10i-4i^2)}}} Multiply.



{{{(10-4i-5i+2(-1))/(25-10i+10i-4(-1))}}} Replace {{{i^2}}} with -1.



{{{(10-4i-5i-2)/(25-10i+10i+4)}}} Multiply



{{{(8-9i)/(29)}}} Combine like terms.



{{{8/29-(9/29)i}}} Break up the fraction.



So {{{(2-i)/(5+2i)=8/29-(9/29)i}}}.