We also know that the powers of $i$ repeat in a cycle: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$, and so on.
To simplify $i^{22}$, we can find the remainder when 22 is divided by 4, since the powers of $i$ repeat every 4 powers.
The remainder when 22 is
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