SOLUTION: i90i91+i92i93 note real numbers are exponents that add up to i to the 366 power

Question 70009: i90i91+i92i93 note real numbers are exponents that add up to i to the 366 power
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Recognize that by definition and
From this we can develop the sequence:

Note that this series is i, -1, -i, 1, i, -1, -i, 1, i, ....
We can use this table along with some rules of exponents to simplify the terms in the problem.
Let's try to simplify . We use one of the laws of exponents to rewrite
the this as . From the above table you can see that
Substitute this to get . We can further use a law of exponents
to factor this term into . But so:

So .
We can use this result to find . Note that . Substitute
-1 for to get .
Then use this result and procedure to find that:

Repeat this process to find that:

Substitute these four results into the original problem:

The substitution results in:

The answer to your problem is 2i.
Hope this helps.

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