Question 248065
{{{(5+6i)/(5+3i)}}} Start with the given expression.



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



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



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



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



{{{(25-15i+30i-18i^2)/(25-15i+15i-9i^2)}}} Multiply.



{{{(25-15i+30i-18(-1))/(25-15i+15i-9(-1))}}} Replace {{{i^2}}} with {{{-1}}}



{{{(25-15i+30i+18)/(25-15i+15i+9)}}} Multiply



{{{(43+15i)/(34)}}} Combine like terms.



{{{43/34+(15/34)i}}} Break up the fraction.



So {{{(5+6i)/(5+3i)=43/34+(15/34)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=43/34}}} and {{{b=15/34}}}