What is the square root of (-i)?

Asked by rhariharan | 23rd 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  | 23rd Aug, 2009, 06:25: PM

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