Question 303828
{{{(2-5i)/(4+2i)}}} Start with the given expression.



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



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



{{{((2)(4)+(2)(-2i)+(-5i)(4)+(-5i)(-2i))/((4+2i)(4-2i))}}} FOIL the numerator.



{{{((2)(4)+(2)(-2i)+(-5i)(4)+(-5i)(-2i))/((4)(4)+(4)(-2i)+(2i)(4)+(2i)(-2i))}}} FOIL the denominator.



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



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



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



{{{(-2-24i)/(20)}}} Combine like terms.



{{{(-2)/(20)+((-24)/(20))i}}} Break up the fraction.



{{{-1/10-(6/5)i}}} Reduce.



So {{{(2-5i)/(4+2i)=-1/10-(6/5)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=-1/10}}} and {{{b=-6/5}}}