SOLUTION: Simplify (4+i) (5-2i)

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Question 559909: Simplify (4+i) (5-2i)
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!
%284%2Bi%29%2A%285-2i%29 Start with the given expression.


%284%29%285%29%2B%284%29%28-2i%29%2B%28i%29%285%29%2B%28i%29%28-2i%29 FOIL.


20-8i%2B5i-2i%5E2 Multiply.


20-8i%2B5i-2%28-1%29 Replace i%5E2 with -1. Note: i%5E2=-1.


20-8i%2B5i%2B2 Multiply.


22-3i Combine like terms.


So %284%2Bi%29%2A%285-2i%29=22-3i.


So the expression is now in standard form a%2Bbi where a=22 and b=-3
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