SOLUTION: Please help with equation: Rationalise the complex quotients: 3i^12-i^9 /2i+1

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Question 963235: Please help with equation: Rationalise the complex quotients: 3i^12-i^9 /2i+1
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Do you really have this:
%283i%5E12-i%5E9%29+%2F%282i%2B1%29

First, handle the exponentiated i terms.
i=i
i%5E2=-1
i%5E3=-i
i%5E4=1
and this cycle continues back through i, and so on.

%283%2A1-%28-1%29%29%2F%282i%2B1%29.

%283%2B1%29%2F%282i%2B1%29

4%2F%282i%2B1%29

NOW, multiply the expression by 1=%282i-1%29%2F%282i-1%29, because 2i-1 is the "CONJUGATE" of 2i+1. You will take advantage of the Difference Of Squares.