SOLUTION: 5. Simplify {{{(6+4i)(7-3i)}}}

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Question 143733: 5. Simplify %286%2B4i%29%287-3i%29



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%286%2B4i%29%287-3i%29 Start with the given expression


Now let's FOIL the expression



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


%28highlight%286%29%2B4i%29%28highlight%287%29-3i%29 Multiply the First terms:%286%29%2A%287%29=42


%28highlight%286%29%2B4i%29%287%2Bhighlight%28-3i%29%29 Multiply the Outer terms:%286%29%2A%28-3i%29=-18i


%286%2Bhighlight%284i%29%29%28highlight%287%29-3i%29 Multiply the Inner terms:%284i%29%2A%287%29=28i


%286%2Bhighlight%284i%29%29%287%2Bhighlight%28-3i%29%29 Multiply the Last terms:%284i%29%2A%28-3i%29=-12i%5E2=-12%28-1%29=12 note: remember, i%5E2=-1


42-18i%2B28i%2B12 Now collect every term to make a single expression



54%2B10i Combine like terms


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Answer:
So %286%2B4i%29%287-3i%29 foils and simplifies to 54%2B10i

In other words, %286%2B4i%29%287-3i%29=54%2B10i