Question 195738

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



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



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



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



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



{{{(36+18i+18i+9i^2)/(36+18i-18i-9i^2)}}} Multiply.



{{{(27+36i)/(45)}}} Combine like terms.



{{{(27)/(45)+((36)/(45))i}}} Break up the fraction.



{{{3/5+(4/5)i}}} Reduce.



So {{{(6+3i)/(6-3i)=3/5+(4/5)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=3/5}}} and {{{b=4/5}}}