SOLUTION: What is 2/3+i equivalent to?? I've forgotten complex number operations!

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Question 335421: What is 2/3+i equivalent to?? I've forgotten complex number operations!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%283%2Bi%29 Start with the given expression.


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


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


%28%282%29%283%29%2B%282%29%28-i%29%29%2F%28%283%2Bi%29%283-i%29%29 Distribute.


FOIL the denominator.


%286-2i%29%2F%289-3i%2B3i-i%5E2%29 Multiply.


%286-2i%29%2F%289-3i%2B3i-%28-1%29%29 Replace i%5E2 with -1.


%286-2i%29%2F%289-3i%2B3i%2B1%29 Rewrite -(-1) as +1


%286-2i%29%2F%2810%29 Combine like terms.


%286%29%2F%2810%29-%28%282%29%2F%2810%29%29i Break up the fraction.


3%2F5-%281%2F5%29i Reduce.


So 2%2F%283%2Bi%29=3%2F5-%281%2F5%29i.


So the expression is now in standard form a%2Bbi where a=3%2F5 and b=-1%2F5