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How do you prove that the quantity sqrt of 2 plus the sqrt of -2 all divided by 2 is a square root of i?
Wiki User
∙ 13y ago
Compute the square and see what you get: Let s be the sq rt of 2, then is = the sq rt of -2.
[ (s + is)/2 ]2= [ s2 + 2ssi + (is)2 ] / 4 = [2 +2(2) i -2] /4 = 4i / 4 = i using the
fact that ss = 2 and (is)2 = i2s2 = (-1)(2) = -2.
Wiki User
∙ 13y ago
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