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If the imaginary part of the complex num...

If the imaginary part of the complex number `(z-1)(cos alpha-i sin alpha) +(z-1)^-1 (cos alpha+i sin alpha)` is zero, then which of the following options are correct? a) `|z|=1` b) `|z-1|=1` c) `arg(z)=alpha` d) `arg(z-1)=alpha`

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