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Let alpha+ibeta be a complex number and ...

Let `alpha+ibeta` be a complex number and let `x+iy=e^(alpha+ibeta)` where `(x,y,alpha,beta in R)` then we define `log_e(x+iy)=alpha+ibeta`
`x+iy=re^(itheta)`,where `r=sqrt(x^2+y^2),theta=tan^(-1)(y/x), alpha+ibeta=log_e(x+iy)=log_e(r.e^(itheta)=log_er+itheta` so `log_e(x+iy)=log_er+itheta`
`log_e(z)=log_eabsz+iarg(z)`
`log_e(-i)` equals

A

`(pii)/2`

B

`pii`

C

`(-pii)/2`

D

0

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The correct Answer is:
C
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