SOLUTION: (2 - i)/ (5 + 2i)

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Question 306966: (2 - i)/ (5 + 2i)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282-i%29%2F%285%2B2i%29 Start with the given expression.


%28%282-i%29%2F%285%2B2i%29%29%28%285-2i%29%2F%285-2i%29%29 Multiply the fraction by %285-2i%29%2F%285-2i%29.


%28%282-i%29%285-2i%29%29%2F%28%285%2B2i%29%285-2i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2810-4i-5i%2B2i%5E2%29%2F%2825-10i%2B10i-4i%5E2%29 Multiply.


%2810-4i-5i%2B2%28-1%29%29%2F%2825-10i%2B10i-4%28-1%29%29 Replace i%5E2 with -1.


%2810-4i-5i-2%29%2F%2825-10i%2B10i%2B4%29 Multiply


%288-9i%29%2F%2829%29 Combine like terms.


8%2F29-%289%2F29%29i Break up the fraction.


So %282-i%29%2F%285%2B2i%29=8%2F29-%289%2F29%29i.