Question 529806
{{{(5)/(2+4i)}}} Start with the given expression.



{{{((5)/(2+4i))((2-4i)/(2-4i))}}} Multiply the fraction by {{{(2-4i)/(2-4i)}}}.



{{{((5)(2-4i))/((2+4i)(2-4i))}}} Combine the fractions.



{{{(10-20i)/((2+4i)(2-4i))}}} Distribute.



{{{(10-20i)/((2)(2)+(2)(-4i)+(4i)(2)+(4i)(-4i))}}} FOIL the denominator.



{{{(10-20i)/(4-8i+8i-16i^2)}}} Multiply.



{{{(10-20i)/(4-8i+8i-16(-1))}}} Replace {{i^2}}} with -1.



{{{(10-20i)/(4-8i+8i+16)}}} Multiply.



{{{(10-20i)/(20)}}} Combine like terms.



{{{(10)/(20)+((-20)/(20))i}}} Break up the fraction.



{{{1/2-i}}} Reduce.



So {{{(5)/(2+4i)=1/2-i}}}



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