SOLUTION: Write the complex number 2-i (over) 5+i in the usual a + bi form

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Question 189232: Write the complex number
2-i
(over)
5+i
in the usual a + bi form
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%282-i%29%2F%285%2Bi%29 Start with the given expression.


%28%282-i%29%2F%285%2Bi%29%29%28%285-i%29%2F%285-i%29%29 Multiply the fraction by %285-i%29%2F%285-i%29.


%28%282-i%29%285-i%29%29%2F%28%285%2Bi%29%285-i%29%29 Combine the fractions.


%28%282%29%285%29%2B%282%29%28-i%29%2B%28-i%29%285%29%2B%28-i%29%28-i%29%29%2F%28%285%2Bi%29%285-i%29%29 FOIL the numerator.


%28%282%29%285%29%2B%282%29%28-i%29%2B%28-i%29%285%29%2B%28-i%29%28-i%29%29%2F%28%285%29%285%29%2B%285%29%28-i%29%2B%28i%29%285%29%2B%28i%29%28-i%29%29 FOIL the denominator.


%2810-2i-5i%2Bi%5E2%29%2F%2825-5i%2B5i-i%5E2%29 Multiply.


%289-7i%29%2F%2826%29 Combine like terms.


%289%29%2F%2826%29%2B%28%28-7%29%2F%2826%29%29i Break up the fraction.


9%2F26-%287%2F26%29i Reduce.


So %282-i%29%2F%285%2Bi%29=9%2F26-%287%2F26%29i.


So the expression is now in standard form a%2Bbi where a=9%2F26 and b=-7%2F26