SOLUTION: 2-i/3-4i

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Question 240571: 2-i/3-4i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282-i%29%2F%283-4i%29 Start with the given expression.


%28%282-i%29%2F%283-4i%29%29%28%283%2B4i%29%2F%283%2B4i%29%29 Multiply the fraction by %283%2B4i%29%2F%283%2B4i%29.


%28%282-i%29%283%2B4i%29%29%2F%28%283-4i%29%283%2B4i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%286%2B8i-3i-4i%5E2%29%2F%289%2B12i-12i-16i%5E2%29 Multiply.


%286%2B8i-3i-4%28-1%29%29%2F%289%2B12i-12i-16%28-1%29%29 Replace i%5E2 with -1.


%286%2B8i-3i%2B4%29%2F%289%2B12i-12i%2B16%29 Multiply.


%2810%2B5i%29%2F%2825%29 Combine like terms.


%2810%29%2F%2825%29%2B%28%285%29%2F%2825%29%29i Break up the fraction.


2%2F5%2B%281%2F5%29i Reduce.


So %282-i%29%2F%283-4i%29=2%2F5%2B%281%2F5%29i.


So the expression is now in standard form a%2Bbi where a=2%2F5 and b=1%2F5