SOLUTION: 3+i / 2+3i

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Question 198082: 3+i / 2+3i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2Bi%29%2F%282%2B3i%29 Start with the given expression.


%28%283%2Bi%29%2F%282%2B3i%29%29%28%282-3i%29%2F%282-3i%29%29 Multiply the fraction by %282-3i%29%2F%282-3i%29.


%28%283%2Bi%29%282-3i%29%29%2F%28%282%2B3i%29%282-3i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%286-9i%2B2i-3i%5E2%29%2F%284-6i%2B6i-9i%5E2%29 Multiply.


%289-7i%29%2F%2813%29 Combine like terms.


%289%29%2F%2813%29%2B%28%28-7%29%2F%2813%29%29i Break up the fraction.


9%2F13-%287%2F13%29i Reduce.


So %283%2Bi%29%2F%282%2B3i%29=9%2F13-7%2F13i.


So the expression is now in standard form a%2Bbi where a=9%2F13 and b=-7%2F13