SOLUTION: Multiply the complex numbers. (5 + 2i)(2 - i)

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Question 144741: Multiply the complex numbers.


(5 + 2i)(2 - i)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%285%2B2i%29%282-i%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%2B2i%29%28highlight%282%29-i%29 Multiply the First terms:%285%29%2A%282%29=10


%28highlight%285%29%2B2i%29%282%2Bhighlight%28-i%29%29 Multiply the Outer terms:%285%29%2A%28-1i%29=-5i


%285%2Bhighlight%282i%29%29%28highlight%282%29-i%29 Multiply the Inner terms:%282i%29%2A%282%29=4i


%285%2Bhighlight%282i%29%29%282%2Bhighlight%28-i%29%29 Multiply the Last terms:%282i%29%2A%28-1i%29=-2i%5E2=-2%28-1%29=2


10-5i%2B4i%2B2 Now collect every term to make a single expression



12-i Now combine like terms


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Answer:
So %285%2B2i%29%282-i%29 foils and simplifies to 12-i

In other words, %285%2B2i%29%282-i%29=12-i