I propose to add the complex variant of the real $\mathrm{cis}$ function. It would be defined as $\mathrm{cis}\colon\mathbb{C}\to\mathbb{C}$ with

$$\mathrm{cis}(z) = \exp(iz) = \exp(-\mathrm{Im}(z))\mathrm{cis}(\mathrm{Re}(z))$$

This complex $\mathrm{cis}$ function has applications in physics and numerical mathematics.