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)`
if `sin(log_ei)=a+ib` then value of a and b is

Options

A. a=(-1),b=0
B. a=1,b=0
C. a=0,b=(-1)
D. a=0,b=1

Answer

A