SOLUTION: what is sqrt of i?

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Question 5318: what is sqrt of i?
Found 2 solutions by longjonsilver, ichudov:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
very good question!

I would hazard a guess that it is sqrt%28i%29, without it being a cop out.

Jon.

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
well, it is easy.
you need to find numbers a and b such that
+%28a%2Bbi%29%5E2+=+0+%2B+i+
+a%5E2+%2B+2abi+-+b%5E2+=+0+%2B+i
the real parts and imaginary parts should match
%0D%0A++system%28+a%5E2-b%5E2+=+0%2C+%0D%0A++++++++++2ab+=+1%0D%0A+++++++++%29%0D%0A
b+=+1%2F2%5Ca
a%5E2+-+%281%2F2a%29%5E2+=+0
a%5E2+=+1%2F%284a%5E2%29
a%5E4+=+1%2F4
a%5E2+=+1%2F2 (another possibility, a^2 = -1/2, is senseless)
a+=+0%2B-+1%2Fsqrt%282%29
Two solutions: 1%2Fsqrt%282%29%2Bi%2Fsqrt%282%29, -1%2Fsqrt%282%29-i%2Fsqrt%282%29