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 Compute \(i^{11} + i^{16} + i^{21} + i^{26} + i^{31}\)

 Aug 1, 2020
 #1
avatar+1038 
+7

If the power is divisible by 2 and not 4, it is -1.

If the power is divisible by 4, it is 1.

If it satisfys none of those conditions, it is i or -i.

 

(basically, it is a pattern of i, -1, -i, and 1)

 

So, let's see what i^11 is. By running down the list, it satisfys only -i. Which means, i^11 is -i.

i^16 is divisible by 4, so it is 1.

Keep on going like this until you have the answer!

 

:)

 Aug 1, 2020
edited by ilorty  Aug 1, 2020
 #2
avatar+1130 
+2

we know that i^2=-1 so we can have the equation -i+1+i+-1+-i which simplifies to  -i+1+i-1-i where i and -1 cancel and the 1 and -1 cancel to get -i

 

so this equation simplifies to -i

 

\(-i\)

 Aug 2, 2020

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