Simplify $i^7$, where $i = \sqrt{-1}$.
A$i$
B$-1$
C$1$
D$-i$CORRECT
JUPEBMathematicsComplex Numbers
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Why the answer is D, and why the others tempt you.
Powers of $i$ cycle every four: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$. Since $7 = 4 + 3$, $i^7 = i^4 \cdot i^3 = 1 \times (-i) = -i$.
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