SOLUTION: (3+5i)/(3-5i)

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Question 182450: (3+5i)/(3-5i)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2B5i%29%2F%283-5i%29 Start with the given expression.


%28%283%2B5i%29%2F%283-+5i%29%29%28%283%2B5i%29%2F%283%2B5i%29%29 Multiply the fraction by %283%2B5i%29%2F%283%2B5i%29.


%28%283%2B5i%29%283%2B5i%29%29%2F%28%283-5i%29%283%2B5i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%289%2B15i%2B15i%2B25i%5E2%29%2F%289%2B15i-15i-25i%5E2%29 Multiply.


%28-16%2B30i%29%2F%2834%29 Combine like terms.


%28-16%29%2F%2834%29%2B%2830%29%2F%2834%29i Break up the fraction.


-8%2F17%2B%2815%2F17%29i Reduce.


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Answer:


So %283%2B5i%29%2F%283-5i%29=-8%2F17%2B%2815%2F17%29i.


So the expression is now in standard form a%2Bbi where a=-8%2F17 and b=15%2F17