Alg6.1.1

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Considering that:

\sqrt{-1} = i^1 = i

and that:

i^2 = \sqrt{-1^2} = -1,

i^3 = \sqrt{-1^2}\cdot\sqrt{-1} = -1\cdot i = -i,

i^4 = \sqrt{-1^2}\cdot\sqrt{-1^2} = -1\cdot -1 = 1,

then,

i^{17} = i\cdot(i^4)^4 = i\cdot (1)^4 = i\,

Just take the exponent, find the remainder after dividing by 4 (the modulus) and the exponent of 1, 2, 3, or 4 tells you what you have. All the other powers of 4 will just be 1 \cdot 1 \cdot 1 \cdot ..., and can be discarded.


Main Page : Algebra : Complex Numbers

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