These are not equivalent because `cis(pi/2) = i`

whereas `sign(pi/2) = 1`

.

On the subject of `sign`

for complex numbers see recent discussion on the numpy mailing list about changing the convention used there.

Generally the idea when extending to the complex case is that `abs(z)*sign(z) == z`

so `sign(z)`

retains the information discarded by `abs(z)`

.