if 1^2 = -1 then what does i^5+i^6+i^7= anyone give me somewhere to start on this one

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- Aug 19th 2009, 09:22 PMnetbookimaginary number
if 1^2 = -1 then what does i^5+i^6+i^7= anyone give me somewhere to start on this one

- Aug 19th 2009, 09:57 PMJG89
I'm sure it was just a typo, but it should be . To compute just calculate what is, what is and what is, then add them together.

For example, you know that , so . Continuing on, and continue in this process. - Aug 19th 2009, 11:10 PMbandedkrait
A simple but interesting result which we obtain from above is that :

**The sum of any 4 consecutive powers of is equal to zero.**

Hence using this result,

Hence the value of the given expression is merely

i.e. http://www.mathhelpforum.com/math-he...acaf41ab-1.gif=

and we know,

Hence the required answer is - Aug 19th 2009, 11:18 PMnetbook
so how do we know that i^4 = 1 and why then would -i^8 = -1

- Aug 19th 2009, 11:25 PMbandedkrait
since

Square both sides,

Now, square both sides again,

so clearly - Aug 19th 2009, 11:33 PMnetbook
ok thanks again for your patience