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i^23 in standard a+bi form
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\[i^{23}=i^{22}\times i\]\[i ^{22}\times i =-1\times i=-i\]
just to clarify: \[i^{22} = (i^2)^{11} = (-1)^{11} = -1\]
since i^4=1 you can just subtract 4 until you can't anymore.
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