Question 143733
{{{(6+4i)(7-3i)}}} Start with the given expression



Now let's FOIL the expression




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



{{{(highlight(6)+4i)(highlight(7)-3i)}}} Multiply the <font color="red">F</font>irst terms:{{{(6)*(7)=42}}}



{{{(highlight(6)+4i)(7+highlight(-3i))}}} Multiply the <font color="red">O</font>uter terms:{{{(6)*(-3i)=-18i}}}



{{{(6+highlight(4i))(highlight(7)-3i)}}} Multiply the <font color="red">I</font>nner terms:{{{(4i)*(7)=28i}}}



{{{(6+highlight(4i))(7+highlight(-3i))}}} Multiply the <font color="red">L</font>ast terms:{{{(4i)*(-3i)=-12i^2=-12(-1)=12}}} note: remember, {{{i^2=-1}}}



{{{42-18i+28i+12}}} Now collect every term to make a single expression




{{{54+10i}}} Combine like terms



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Answer:

So {{{(6+4i)(7-3i)}}} foils and simplifies to  {{{54+10i}}}


In other words, {{{(6+4i)(7-3i)=54+10i}}}