Powers of i Calculator
MathCalculate any power of the imaginary unit i, using its repeating 4-step cycle.
i^n
The value of i raised to the power n.
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Frequently Asked Questions
Why do powers of i repeat?
i is defined by i^2 = -1. This means i^1=i, i^2=-1, i^3=-i, i^4=1, and then the pattern repeats forever, since i^5 = i^4 * i = 1 * i = i, and so on.
How do you find i raised to a large exponent quickly?
Find the remainder when the exponent is divided by 4. That remainder (0, 1, 2, or 3) tells you exactly where in the 4-step cycle (1, i, -1, -i) the answer falls, no matter how large the original exponent is.
What about negative exponents?
The same 4-step cycle still applies, just counted in the negative direction; i^-1 = -i, i^-2 = -1, and so on, following the identical repeating pattern.
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