Question 316763
{{{(6+3i)/(4-3i)}}} Start with the given expression.



{{{((6+3i)/(4-3i))((4+3i)/(4+3i))}}} Multiply the fraction by {{{(4+3i)/(4+3i)}}}.



{{{((6+3i)(4+3i))/((4-3i)(4+3i))}}} Combine the fractions.



{{{((6)(4)+(6)(3i)+(3i)(4)+(3i)(3i))/((4-3i)(4+3i))}}} FOIL the numerator.



{{{((6)(4)+(6)(3i)+(3i)(4)+(3i)(3i))/((4)(4)+(4)(3i)+(-3i)(4)+(-3i)(3i))}}} FOIL the denominator.



{{{(24+18i+12i+9i^2)/(16+12i-12i-9i^2)}}} Multiply.



{{{(24+18i+12i+9(-1))/(16+12i-12i-9(-1))}}} Replace {{{i^2}}} with -1.



{{{(24+18i+12i-9)/(16+12i-12i+9)}}} Multiply.



{{{(15+30i)/(25)}}} Combine like terms.



{{{(15)/(25)+((30)/(25))i}}} Break up the fraction.



{{{3/5+(6/5)i}}} Reduce.



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



So the expression is now in standard form {{{a+bi}}} where {{{a=3/5}}} and {{{b=6/5}}}