SOLUTION: May you please help me simplify: (a^4+b^4)/(a^2+b^2) and (3+2i)/(3-2i)? I spent a while looking through previously answered questions but couldn't find a similar enough problem. Th

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Question 33508: May you please help me simplify: (a^4+b^4)/(a^2+b^2) and (3+2i)/(3-2i)? I spent a while looking through previously answered questions but couldn't find a similar enough problem. Thank you for your help.
Found 2 solutions by mukhopadhyay, stanbon:
Answer by mukhopadhyay(490) (Show Source):
You can put this solution on YOUR website!
Are you sure the first problem is written correctly?
(3+2i)/(3-2i)
=[(3+2i)(3+2i)]/[(3-2i)(3+2i)]
= (3+2i)^2/[(3^2-(2i)^2)]
= [9+12i+(2i)^2]/(9+4)
= (5+12i)/13

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1st: If you do the problem using long division you get
Quotient = a^2-b^2 and a Remainder of 2b^2/(a^2+b^2).
2nd: (3+2i)/(3-2i)
Multiply numerator and denominator by (3+2i) to get:
(3+2i)^2/(9+4)
=[9-4+12i]/13
=[5+12i]/13
=(5/13)+(12/13)i
Cheers,
Stan H.