SOLUTION: 2+i/7-5i

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Question 318436: 2+i/7-5i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bi%29%2F%287-5i%29 Start with the given expression.


%28%282%2Bi%29%2F%287-5i%29%29%28%287%2B5i%29%2F%287%2B5i%29%29 Multiply the fraction by %287%2B5i%29%2F%287%2B5i%29.


%28%282%2Bi%29%287%2B5i%29%29%2F%28%287-5i%29%287%2B5i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2814%2B10i%2B7i%2B5i%5E2%29%2F%2849%2B35i-35i-25i%5E2%29 Multiply.


%2814%2B10i%2B7i%2B5%28-1%29%29%2F%2849%2B35i-35i-25%28-1%29%29 Replace i%5E2 with -1.


%2814%2B10i%2B7i-5%29%2F%2849%2B35i-35i%2B25%29 Multiply.


%289%2B17i%29%2F%2874%29 Combine like terms.


9%2F74%2B%2817%2F74%29i Break up the fraction.


So %282%2Bi%29%2F%287-5i%29=9%2F74%2B%2817%2F74%29i.


So the expression is now in standard form a%2Bbi where a=9%2F74 and b=17%2F74