What is the value of i 20+1? 1 –1 –i i

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What is the value of i 20+1? 1 –1 –i i

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I got 2 but thats not an option?
maybe you meant \(\large\color{black}{ \displaystyle i^{20+1} }\) ?
yes! sorry

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yes, it is alright. next when you want to write that, just say i^(20+1) where ^ indicates an exponent, and (...) tell you what your exponent is.
Anyway,
Can you tell me what does \(\large\color{black}{ \displaystyle i^4 }\) equal to?
oh duh, answer is i
yes, that is 1.
So, \(\large\color{black}{ \displaystyle i^{20+1}=i^{20} \times i^1=i^{4\times 5}\times i=\left(i^4\right)^5\times i = 1^5\times i=? }\)
well, you probably know anyway that \(\large\color{black}{ \displaystyle i^{4n}=1 }\) \(\large\color{black}{ \displaystyle i^{4n+1}=i }\) \(\large\color{black}{ \displaystyle i^{4n+2}=-1 }\) \(\large\color{black}{ \displaystyle i^{4n+3}=-i }\) and again restarting the cycle, \(\large\color{black}{ \displaystyle i^{4n+4}=1 }\) and so on... (this is true for any whole number powers of i)
(saying, for any whole number n)
If you got any questions, please ask...

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