SOLUTION: PLease help to simplify -3i^4 + 5i^3 DIVIDED BY 6i^2 - 7i

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Question 67309This question is from textbook An Incremental Development
: PLease help to simplify
-3i^4 + 5i^3
DIVIDED BY
6i^2 - 7i This question is from textbook An Incremental Development

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3i^4 + 5i^3
DIVIDED BY
6i^2 - 7i
:
It helps to know the pattern of how the successive powers of i are simplified:
i^1 = i
i^2 = -1
i^3 = i^2 * i = -i
i^4 = i^2 * i^2 = -1 * -1 = +1
i^5 = i * i^4 = i*1 = i
i^6 = i^2 * i^4 = -1 * 1 = -1
:
Rewrite the equation using this information:
3(1) + 5(-i)
------------
6(-1) - 7i
:
You end up with:
%28%283+-+5i%29%29%2F%28%28-6+-+7i%29%29
:
we can further simplify (get rid of i in the denominator) by mult the denominator by it's conjugate:
%28%283+-+5i%29%29%2F%28%28-6+-+7i%29%29 * %28%28-6+%2B+7i%29%29%2F%28%28-6+%2B+7i%29%29 = %28%28-18+%2B+51i+-+35i%5E2%29%29%2F%28%2836+-+49i%5E2%29%29 = %28%28-18+%2B+51i+-+35%28-1%29%29%29%2F%28%2836+-+49%28-1%29%29%29 = %28%28-18+%2B+51i+%2B+35%29%29%2F%28%2836+%2B+49%29%29 =
:
%28%2817+%2B+51i%29%29%2F%28%2885%29%29 = %28%281+%2B+3i%29%29%2F%28%285%29%29; Notice we can reduce the fraction by dividing by 17