SOLUTION: May I have some help solving this expression? Evaluate the expression and write the result in the form a + bi. (5-sqrt(-25))/(5+sqrt(-25))

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Question 120617: May I have some help solving this expression?
Evaluate the expression and write the result in the form a + bi.
(5-sqrt(-25))/(5+sqrt(-25))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285-sqrt%28-25%29%29%2F%285%2Bsqrt%28-25%29%29+ Start with the given expression



Multiply the fraction by %285-sqrt%28-25%29%29%2F%285-sqrt%28-25%29%29



%285-sqrt%28-25%29%29%285-sqrt%28-25%29%29%2F%285%2Bsqrt%28-25%29%29%285-sqrt%28-25%29%29 Combine the fractions



Foil the denominator



%285-sqrt%28-25%29%29%285-sqrt%28-25%29%29%2F%2850%29 Combine like terms



%2825-10sqrt%28-25%29-25%29%2F%2850%29 Foil the numerator



%28-10sqrt%28-25%29%29%2F%2850%29 Combine like terms



%28-10%2A5i%29%2F%2850%29 Simplify sqrt%28-25%29 to get 5i




%28-50i%29%2F%2850%29 Multiply


-i Reduce


So %285-sqrt%28-25%29%29%2F%285%2Bsqrt%28-25%29%29+ simplifies to -i


So the answer also looks like 0-1i which is now in a%2Bbi form where a=0 and b=-1