SOLUTION: Solve i^-4003

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Question 542668: Solve i^-4003
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (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) About Me  (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
+i%5E%28-4003%29+
This is a vector that rotates in the opposite direction
the sequence is:
-i, -1, i, 1
The vector goes around +4003%2F4+ times, because
every 4 steps brings it back to +-i+
+4003%2F4+=+1000+ with a remainder of +3+
1 step puts me at -1
2 steps puts me at +i+
3 steps puts me at +1+
+i%5E%28-4003%29+=+1+
Hope I got it. You might want
another opinion in case I messed up.