SOLUTION: find the value of the following complex number: I^5

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Question 802335: find the value of the following complex number: I^5
Found 2 solutions by MathLover1, DrBeeee:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

you need to use i, not I
as you know, by definition, i=sqrt%28-1%29 or i%5E2=-1
i%5E5=i%5E2%2Ai%5E2%2Ai=%28-1%29%2A%28-1%29%2Ai=1%2Ai=i

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
What is i%5E5?
Let
(1) i+=+sqrt%28-1%29
Then
(2) i%5E5+=+%28-1%29%5E%285%2F2%29 or
(3) i%5E5+=+sqrt%28%28-1%29%5E%285%29%29 or
(4) i%5E5+=+sqrt%28-1%29 or
(5) i%5E5+=+i
Another way to show this is to use the polar form of i as
(6) i = 1 @ 90 deg
Then
(7) i%5E5+=+1%5E5 @ 5*90 deg or
(8) i%5E5+=+1 @ 450 deg or
(9) i%5E5+=+1 @ 90 deg or
(10)i%5E5+=+i