Question 389787
{{{(5+6i)/(4-2i)}}} Start with the given expression.



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



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



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



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



{{{(20+10i+24i+12i^2)/(16+8i-8i-4i^2)}}} Multiply.



{{{(20+10i+24i+12(-1))/(16+8i-8i-4(-1))}}} Replace {{{i^2}}} with -1.



{{{(20+10i+24i-12)/(16+8i-8i+4)}}} Multiply.



{{{(8+34i)/(20)}}} Combine like terms.



{{{(8)/(20)+((34)/(20))i}}} Break up the fraction.



{{{2/5+(17/10)i}}} Reduce.



So {{{(5+6i)/(4-2i)=2/5+(17/10)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=2/5}}} and {{{b=17/10}}}



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