SOLUTION: (1+2i)/(3-4i)+(2-i)/5i

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Question 933635: (1+2i)/(3-4i)+(2-i)/5i


Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2B2i%29%2F%283-4i%29%2B%282-i%29%2F5i

%281%2B2i%295i%2F5i%283-4i%29%2B%28%282-i%29%283-4i%29%29%2F%285i%283-4i%29%29

%285i-10%29%2F%2815i%2B20%29%2B%282-11i%29%2F%2815i%2B20%29...common denominator is %2815i%2B20%29, so add numerators

%285i-10%2B2-11i%29%2F%2815i%2B20%29

%28-8-6i%29%2F%2815i%2B20%29....multiply both by %2815i-20%29%29 to eliminate i from denominator

%28%28-8-6i%29%2815i-20%29%29%2F%28%2815i%2B20%29%2815i-20%29%29

%28-120i%2B160-90i%5E2%2B120i%29%2F%28%2815i%29%5E2-20%5E2%29%29

%28160-90%28-1%29%29%2F%28%2815i%29%5E2-20%5E2%29%29

250%2F%28-225-400%29%29

250%2F%28-625%29%29........divide both by 125

-cross%28250%292%2Fcross%28625%295%29

-2%2F5%29


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(1+2i)/(3-4i)+(2-i)/5i
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Rationalize the DEN's first
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(1+2i)*(3+4i)/25 + (2-i)*i/(-5)
= (3 + 10i - 8)/25 + (2i+i)/(-5)
= (3 + 10i - 8)/25 - (1 + 2i)/5
= (-5 + 10i)/25 - (1 - 2i)/5
= (-1 + 2i)/5 - (1 + 2i)/5
= -2/5