SOLUTION: The value of √i =±1+I/√2 How come?????

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Question 965200: The value of √i =±1+I/√2
How come?????
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
i=0%2Bi=cos%2890%29%2Bisin%2890%29
So then,
sqrt%28i%29=%28cos%2890%29%2Bisin%2890%29%29%5E%281%2F2%29
Using DeMoivre's theorem,
sqrt%28i%29=cos%28%2890%2Bk%2A%28360%29%29%2F2%29%2Bisin%28%2890%2Bk%2A%28360%29%29%2F2%29 for k=0 and k=1.
.
.
k=0
sqrt%28i%29=cos%2890%2F2%29%2Bisin%2890%2F2%29
sqrt%28i%29=cos%2845%29%2Bisin%2845%29
sqrt%28i%29=%28sqrt%282%29%29%2F2%29%281%2Bi%29
.
.
k=1
sqrt%28i%29=cos%28450%2F2%29%2Bisin%28450%2F2%29
sqrt%28i%29=cos%28225%29%2Bisin%28225%29
sqrt%28i%29=-%28sqrt%282%29%2F2%29%281%2Bi%29