Question 195529
{{{(16+4i)/(16-4i)}}} Start with the given expression.



{{{((16+4i)/(16-4i))((16+4i)/(16+4i))}}} Multiply the fraction by {{{(16+4i)/(16+4i)}}}.



{{{((16+4i)(16+4i))/((16-4i)(16+4i))}}} Combine the fractions.



{{{((16)(16)+(16)(4i)+(4i)(16)+(4i)(4i))/((16-4i)(16+4i))}}} FOIL the numerator.



{{{((16)(16)+(16)(4i)+(4i)(16)+(4i)(4i))/((16)(16)+(16)(4i)+(-4i)(16)+(-4i)(4i))}}} FOIL the denominator.



{{{(256+64i+64i+16i^2)/(256+64i-64i-16i^2)}}} Multiply.



{{{(240+128i)/(272)}}} Combine like terms.



{{{(240)/(272)+((128)/(272))i}}} Break up the fraction.



{{{15/17+(8/17)i}}} Reduce.



So {{{(16+4i)/(16-4i)=15/17+(8/17)i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=15/17}}} and {{{b=8/17}}}