Prelude Data.Complex> 0**2

0.0

Prelude Data.Complex> 0**2 :: Complex Double

NaN :+ NaN

Prelude Data.Complex> exp $ 2 * log 0 :: Complex Double

NaN :+ NaN

Prelude Data.Complex> log 0 :: Complex Double

(-Infinity) :+ 0.0

Prelude Data.Complex> 2 * it :: Complex Double

(-Infinity) :+ NaN

Prelude Data.Complex> exp it :: Complex Double

NaN :+ NaN

So Complex uses the default implementation of **. Then when 2*(-inf :+ 0) is evaluated. We do (2 * -inf - 0*0) :+ (2*0 + -inf*0). Which because of -inf*0 sets the imaginary part to NaN. 

Then exp (-inf :+ NaN) = exp x cos y :+ exp x sin y which becomes 0 * cos NaN :+ 0 * sin NaN. So we end up with NaN :+ NaN.

So is there a library I should be using, or is this a bug?