$$\operatorname{re}{\left(z\right)} \operatorname{sign}{\left(z \right)} + \left|{z}\right|$$
2*(DiracDelta(z)*re(z) + sign(z))
$$2 \left(\operatorname{re}{\left(z\right)} \delta\left(z\right) + \operatorname{sign}{\left(z \right)}\right)$$
2*(3*DiracDelta(z) + DiracDelta(z, 1)*re(z))
$$2 \left(\operatorname{re}{\left(z\right)} \delta^{\left( 1 \right)}\left( z \right) + 3 \delta\left(z\right)\right)$$