SOLUTION: Divide: (6 + 3i)/6 – 3i)

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Question 195738: Divide: (6 + 3i)/6 – 3i)
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

%286%2B3i%29%2F%286-3i%29 Start with the given expression.


%28%286%2B3i%29%2F%286-3i%29%29%28%286%2B3i%29%2F%286%2B3i%29%29 Multiply the fraction by %286%2B3i%29%2F%286%2B3i%29.


%28%286%2B3i%29%286%2B3i%29%29%2F%28%286-3i%29%286%2B3i%29%29 Combine the fractions.


%28%286%29%286%29%2B%286%29%283i%29%2B%283i%29%286%29%2B%283i%29%283i%29%29%2F%28%286-3i%29%286%2B3i%29%29 FOIL the numerator.


%28%286%29%286%29%2B%286%29%283i%29%2B%283i%29%286%29%2B%283i%29%283i%29%29%2F%28%286%29%286%29%2B%286%29%283i%29%2B%28-3i%29%286%29%2B%28-3i%29%283i%29%29 FOIL the denominator.


%2836%2B18i%2B18i%2B9i%5E2%29%2F%2836%2B18i-18i-9i%5E2%29 Multiply.


%2827%2B36i%29%2F%2845%29 Combine like terms.


%2827%29%2F%2845%29%2B%28%2836%29%2F%2845%29%29i Break up the fraction.


3%2F5%2B%284%2F5%29i Reduce.


So %286%2B3i%29%2F%286-3i%29=3%2F5%2B%284%2F5%29i.


So the expression is now in standard form a%2Bbi where a=3%2F5 and b=4%2F5