SOLUTION: Solve i^-4003

Question 542668: Solve i^-4003
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve i^-4003
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Note i^-1 = 1/i = i^3
Keep in mind that i^4 = 1
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Your problem:
i^(-4003) = (i^3)^(4003) = i^(12009= i^9 = i^1 = i
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Cheers,
Stan
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
When plotting imaginary and real numbers, the
vertical axes are imaginary.
For a rotating vector of length 1, the sequence is:
i, -1, -i, 1
and this just keeps repeating as the vector rotates

This is a vector that rotates in the opposite direction
the sequence is:
-i, -1, i, 1
The vector goes around times, because
every 4 steps brings it back to
with a remainder of
1 step puts me at
2 steps puts me at
3 steps puts me at

Hope I got it. You might want
another opinion in case I messed up.

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