SOLUTION: how do you simplify this?? 3+i ----- <--- represents a fraction bar 5-6i

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Question 243667: how do you simplify this??
3+i
----- <--- represents a fraction bar
5-6i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2Bi%29%2F%285-6i%29 Start with the given expression.


%28%283%2Bi%29%2F%285-6i%29%29%28%285%2B6i%29%2F%285%2B6i%29%29 Multiply the fraction by %285%2B6i%29%2F%285%2B6i%29.


Note: 5+6i is the complex conjugate of 5-6i. Multiplying a complex number with its conjugate will result in a real number.


%28%283%2Bi%29%285%2B6i%29%29%2F%28%285-6i%29%285%2B6i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%2815%2B18i%2B5i%2B6i%5E2%29%2F%2825%2B30i-30i-36i%5E2%29 Multiply.


%2815%2B18i%2B5i%2B6%28-1%29%29%2F%2825%2B30i-30i-36%28-1%29%29 Replace i%5E2 with -1 (since i%5E2=-1).


%2815%2B18i%2B5i-6%29%2F%2825%2B30i-30i%2B36%29 Multiply


%289%2B23i%29%2F%2861%29 Combine like terms.


9%2F61%2B%2823%2F61%29i Break up the fraction.


So %283%2Bi%29%2F%285-6i%29=9%2F61%2B%2823%2F61%29i.


So the expression is now in standard form a%2Bbi where a=9%2F61 and b=23%2F61