Question 451157
{{{(4+2i)/(5-6i)}}} Start with the given expression.



{{{((4+2i)/(5-6i))((5+6i)/(5+6i))}}} Multiply the fraction by {{{(5+6i)/(5+6i)}}}.



{{{((4+2i)(5+6i))/((5-6i)(5+6i))}}} Combine the fractions.



{{{((4)(5)+(4)(6i)+(2i)(5)+(2i)(6i))/((5-6i)(5+6i))}}} FOIL the numerator.



{{{((4)(5)+(4)(6i)+(2i)(5)+(2i)(6i))/((5)(5)+(5)(6i)+(-6i)(5)+(-6i)(6i))}}} FOIL the denominator.



{{{(20+24i+10i+12i^2)/(25+30i-30i-36i^2)}}} Multiply.



{{{(20+24i+10i+12(-1))/(25+30i-30i-36(-1))}}} Replace {{{i^2}}} with -1.



{{{(20+24i+10i-12)/(25+30i-30i+36)}}} Multiply.



{{{(8+34i)/(61)}}} Combine like terms.



{{{(8)/(61)+((34)/(61))i}}} Break up the fraction.



{{{8/61+(34/61)i}}} Reduce.



So {{{(4+2i)/(5-6i)=8/61+(34/61)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=8/61}}} and {{{b=34/61}}}