Question 231250: find a complex number, in a+bi form, such that radical i = a+bi.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find a complex number, in a+bi form, such that radical i = a+bi.
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0+i = (cos(90) + isin(90)
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Sqrt(i) = (cos(90+360n) + isin(90+360n))^(1/2)
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sqrt(i) = (cos[(90+360n)/2] + isin[(90+360n)/2]
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Let n = 0, then:
sqrt(i) = [cos(45) + isin(45)] = (sqrt(2))/2 + i(sqrt(2))/2
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Let n = 1, then:
sqrt(i) = [cos(225)+isin(225) = (-sqrt(2)/2)+i(sqrt(2))/2
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Both answers are in the form a+bi
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Cheers,
Stan H.
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