SOLUTION: The problem is i to the -10th power. I don't even know how to begin to start. The example in the book of i to the -3rd=i to the -4 x i and I don't understand why. Can you give m

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The problem is i to the -10th power. I don't even know how to begin to start. The example in the book of i to the -3rd=i to the -4 x i and I don't understand why. Can you give m      Log On


   

Question 96475This question is from textbook College Algebra
: The problem is i to the -10th power. I don't even know how to begin to start. The example in the book of i to the -3rd=i to the -4 x i and I don't understand why. Can you give me another example that might work like this one? This question is from textbook College Algebra

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i+=+sqrt%28-1%29+
i%5E2+=+-1+
i%5E3+=+%28i%29%28i%5E2%29+ giving i%5E3+=+-i+
i%5E4+=+%28i%5E2%29%5E2+ giving i%5E4+=+%28-1%29%5E2+ and hence i%5E4+=+1+

After this, the next powers just return through the same 4 values, so i%5E5+=+i etc.

So, i%5E10+ is the same as i%5E2 which is -1.

Anything as a negative power, like a%5E%28-n%29 means 1%2F%28a%5En%29, so 1/(-1) is -1. That is your answer.

cheers
jon