Theory of Intelligence
11TH•Mathematics•Complex Numbers•Exercise 1.1

Theory

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Theory

Write n = 4q + r where r is the remainder when dividing by 4.

Then:

TEXT
i^n = i^{4q+r} = (i^4)^q i^r = 1^q i^r = i^r

So the value depends only on r = 0,1,2,3.

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