On the complex plane, I have a transformation "T" such that :
$z' = (m+i)z + m - 1 - i$ ($z'$ is the image and $z$ the preimage, $z$ and $z'$ are both complex number)
and $m$ is a real number.
I'd need to determine "$m$" such that this transformation "T" is a rotation.
I know a rotation can be written under the form : $z'- w = k (z - w)$ with "$w$" the complex number associated with the center and "$k$" a complex number modulus 1. But I can't find how to put "T" under the form of a rotation.
Some hint would be very appreciated, Thanks.