SOLUTION: 5+6i/5+3i

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Question 248065: 5+6i/5+3i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2B6i%29%2F%285%2B3i%29 Start with the given expression.


%28%285%2B6i%29%2F%285%2B3i%29%29%28%285-3i%29%2F%285-3i%29%29 Multiply the fraction by %285-3i%29%2F%285-3i%29.


%28%285%2B6i%29%285-3i%29%29%2F%28%285%2B3i%29%285-3i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2825-15i%2B30i-18i%5E2%29%2F%2825-15i%2B15i-9i%5E2%29 Multiply.


%2825-15i%2B30i-18%28-1%29%29%2F%2825-15i%2B15i-9%28-1%29%29 Replace i%5E2 with -1


%2825-15i%2B30i%2B18%29%2F%2825-15i%2B15i%2B9%29 Multiply


%2843%2B15i%29%2F%2834%29 Combine like terms.


43%2F34%2B%2815%2F34%29i Break up the fraction.


So %285%2B6i%29%2F%285%2B3i%29=43%2F34%2B%2815%2F34%29i.


So the expression is now in standard form a%2Bbi where a=43%2F34 and b=15%2F34