SOLUTION: i^91=? This question was asked previously (question 3340), and the given soluttion was to find where i^91 came in the cycle of i. However I learned another way to do it, and I was

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: i^91=? This question was asked previously (question 3340), and the given soluttion was to find where i^91 came in the cycle of i. However I learned another way to do it, and I was      Log On


   

Question 4632: i^91=?
This question was asked previously (question 3340), and the given soluttion was to find where i^91 came in the cycle of i. However I learned another way to do it, and I was wondering if it is correct.
Take the given question i^91:
i^91 = i^90 + 1
= i^90 * i^1
= (i^2)^45*i^1
= -1^45 * i^1
= -1 * i
= -i
Found 2 solutions by longjonsilver, khwang:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
this line: i^91 = i^90 + 1 is not needed (and is in fact incorrect). Take it out then the rest is a perfect answer, yes. Well done.

Jon.

Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Since 91 = 3 mod 4
i^91 = i^3 = -i

That's the whole story for this kind of baby math.
Forget any solution more than two lines.
If you still confused, think more and work hard
Kenny