Question 307026
{{{(3i)/(7-8i)}}} Start with the given expression.



{{{((3i)/(7-8i))((7+8i)/(7+8i))}}} Multiply the fraction by {{{(7+8i)/(7+8i)}}}.



{{{((3i)(7+8i))/((7-8i)(7+8i))}}} Combine the fractions.



{{{((3i)(7)+(3i)(8i))/((7-8i)(7+8i))}}} Distribute.



{{{((3i)(7)+(3i)(8i))/((7)(7)+(7)(8i)+(-8i)(7)+(-8i)(8i))}}} FOIL the denominator.



{{{(21i+24i^2)/(49+56i-56i-64i^2)}}} Multiply.



{{{(21i+24(-1))/(49+56i-56i-64(-1))}}} Replace {{{i^2}}} with -1.



{{{(21i-24)/(49+56i-56i+64)}}} Multiply



{{{(-24+21i)/(113)}}} Rearrange and combine like terms.



{{{-24/113+(21/113)i}}}  Break up the fraction.



So {{{(3i)/(7-8i)=-24/113+(21/113)i}}}.