CBSE Class 11-science Answered
What is the square root of (-i)?
Asked by rhariharan | 23 Aug, 2009, 02:56: PM
Expert Answer
Euler equation,
eix = cos x + i sin x
einπ/2 = cos nπ/2 + i sin nπ/2 = - i (n = 3, 7, 9....)
Let's select, n = 3
ei3π/2 = cos 3π/2 + i sin 3π/2
ei3π/2 = - i
(ei3π/2)1/2 = ( - i)1/2
( - i)1/2 = ei3π/4 = cos 3π/4 + i sin 3π/4 = (1/
2)( -1 + i)
( - i)1/2 = einπ/4 = cos nπ/4 + i sin nπ/4 (n = 3, 7, 9....)
Regards,
Team,
TopperLearning.
Answered by | 23 Aug, 2009, 06:25: PM
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