SOLUTION: (5-4i)(3+6i)

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Question 128866: (5-4i)(3+6i)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%285-4i%29%283%2B6i%29 Start with the given expression


Now let's FOIL the expression



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


%28highlight%285%29-4i%29%28highlight%283%29%2B6i%29 Multiply the First terms:%285%29%2A%283%29=15


%28highlight%285%29-4i%29%283%2Bhighlight%286i%29%29 Multiply the Outer terms:%285%29%2A%286i%29=30i


%285%2Bhighlight%28-4i%29%29%28highlight%283%29%2B6i%29 Multiply the Inner terms:%28-4i%29%2A%283%29=-12i


%285%2Bhighlight%28-4i%29%29%283%2Bhighlight%286i%29%29 Multiply the Last terms:%28-4i%29%2A%286i%29=-24i%5E2


15%2B30i-12i-24i%5E2 Now collect every term to make a single expression



18i-24i%5E2%2B15 Now combine like terms


18i-24%28-1%29%2B15 Replace i%5E2 with -1. Remember, i%5E2=-1


18i%2B24%2B15 Multiply


39%2B18i Combine like terms


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Answer:
So %285-4i%29%283%2B6i%29 foils and simplifies to 39%2B18i

In other words, %285-4i%29%283%2B6i%29=39%2B18i