Pow and complex infinites in mathjs

For \[r \in [0, \infty) \text { and } \theta \in (-\pi, \pi] \text{ and } k \in \{ -1, 1 \} \]

we have

\[ \begin{aligned} (re^{i\theta})^{k\infty} &= \left\{ \begin{aligned} &1 &&\text{ if }& r &= 1 &&\text{ and }& \theta &= 0 \\ &0 &&\text{ if }& k(r-1) &< 0 && & & \\ &\text{NaN} &&\text{ if }& r &= 1 &&\text{ and }& \theta &\ne 0 \\ &\infty &&\text{ if }& k(r-1) &> 0 &&\text{ and }& \theta &= 0 \\ &\tilde{\infty} &&\text{ if }& k(r-1) &> 0 &&\text{ and }& \theta &\ne 0 \\ \end{aligned} \right. \\ \\ (re^{i\theta})^{ik\infty} &= \left\{ \begin{aligned} &1 &&\text{ if }& r &= 1 &&\text{ and }& \theta &= 0 \\ &0 &&\text{ if }& & && & k\theta &> 0 \\ &\text{NaN} &&\text{ if }& r &\ne 1 &&\text{ and }& \theta &= 0 \\ &\infty &&\text{ if }& r &= 1 &&\text{ and }& k\theta &< 0 \\ &\tilde{\infty} &&\text{ if }& r &\ne 1 &&\text{ and }& k\theta &< 0 \\ \end{aligned} \right. \\ \\ (re^{i\theta})^{\tilde{\infty}} &= \left\{ \begin{aligned} &1 &&\text{ if }& r &= 1 &&\text{ and }& \theta &= 0 \\ &\text{NaN} &&\text{ if }& r &\ne 1 &&\text{ or }& \theta &\ne 0 \\ \end{aligned} \right. \end{aligned} \]

where \(\tilde{\infty}\) is the complex infinity (infinte magnitude and unknown sign).