Question 128866


{{{(5-4i)(3+6i)}}} Start with the given expression



Now let's FOIL the expression




Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(5)-4i)(highlight(3)+6i)}}} Multiply the First terms:{{{(5)*(3)=15}}}



{{{(highlight(5)-4i)(3+highlight(6i))}}} Multiply the Outer terms:{{{(5)*(6i)=30i}}}



{{{(5+highlight(-4i))(highlight(3)+6i)}}} Multiply the Inner terms:{{{(-4i)*(3)=-12i}}}



{{{(5+highlight(-4i))(3+highlight(6i))}}} Multiply the Last terms:{{{(-4i)*(6i)=-24i^2}}}



{{{15+30i-12i-24i^2}}} Now collect every term to make a single expression




{{{18i-24i^2+15}}} Now combine like terms



{{{18i-24(-1)+15}}} Replace {{{i^2}}} with {{{-1}}}. Remember, {{{i^2=-1}}}



{{{18i+24+15}}} Multiply



{{{39+18i}}} Combine like terms



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Answer:

So {{{(5-4i)(3+6i)}}} foils and simplifies to  {{{39+18i}}}


In other words, {{{(5-4i)(3+6i)=39+18i}}}