Question 549789
{{{(5+3i)/(6-2i)}}} Start with the given expression.



{{{((5+3i)/(6-2i))((6+2i)/(6+2i))}}} Multiply the fraction by {{{(6+2i)/(6+2i)}}}.



{{{((5+3i)(6+2i))/((6-2i)(6+2i))}}} Combine the fractions.



{{{((5)(6)+(5)(2i)+(3i)(6)+(3i)(2i))/((6-2i)(6+2i))}}} FOIL the numerator.



{{{((5)(6)+(5)(2i)+(3i)(6)+(3i)(2i))/((6)(6)+(6)(2i)+(-2i)(6)+(-2i)(2i))}}} FOIL the denominator.



{{{(30+10i+18i+6i^2)/(36+12i-12i-4i^2)}}} Multiply.



{{{(30+10i+18i+6(-1))/(36+12i-12i-4(-1))}}} Replace {{{i^2}}} with {{{-1}}}.



{{{(30+10i+18i-6)/(36+12i-12i+4)}}} Multiply



{{{(24+28i)/(40)}}} Combine like terms.



{{{(24)/(40)+((28)/(40))i}}} Break up the fraction.



{{{3/5+(7/10)i}}} Reduce.



So {{{(5+3i)/(6-2i)=3/5+(7/10)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=3/5}}} and {{{b=7/10}}}